TSASSIGNMENT3_ShivaniGoyal_R00183301
Shivani Goyal(R00183301)
17/05/2020
Declaration of Authorship
I, Shivani Goyal , declare that the work presented in it are my own except for others work which is clearly referenced.
Signed: Shivani Goyal
Date: May 24,2020
PART 1 - TIME SERIES ANALYSIS
Loading and installing all the Required packages
library(readr)
library(tidyr)
library(ggplot2)
library(pastecs)
library(dplyr)
library(VIM)
library(corrplot)
library(imputeTS)
library(lubridate)
library(forecast)
library(tseries)1 - Reading the Assignment Dataset. The provided data file is excel file. The structure of the data is corrected by following given steps below:-
- Reading the Assignment Dataset
Assignment_Data <- read_csv("E:/shivani_timeseries/Assignment Data.csv", col_names = FALSE)
Assignment_Data<- as.data.frame(Assignment_Data)
head(Assignment_Data)## X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18
## 1 1/1/1998 0.8 1.8 2.4 2.1 2 2.1 1.5 1.7 1.9 2.3 3.7 5.5 5.1 5.4 5.4 4.7 4.3
## 2 1/2/1998 2.8 3.2 3.3 2.7 3.3 3.2 2.9 2.8 3.1 3.4 4.2 4.5 4.5 4.3 5.5 5.1 3.8
## 3 1/3/1998 2.9 2.8 2.6 2.1 2.2 2.5 2.5 2.7 2.2 2.5 3.1 4 4.4 4.6 5.6 5.4 5.2
## 4 1/4/1998 4.7 3.8 3.7 3.8 2.9 3.1 2.8 2.5 2.4 3.1 3.3 3.1 2.3 2.1 2.2 3.8 2.8
## 5 1/5/1998 2.6 2.1 1.6 1.4 0.9 1.5 1.2 1.4 1.3 1.4 2.2 2 3 3 3.1 3.1 2.7
## 6 1/6/1998 3.1 3.5 3.3 2.5 1.6 1.7 1.6 1.6 2.3 1.8 2.5 3.9 3.4 2.7 3.4 2.5 2.2
## X19 X20 X21 X22 X23 X24 X25 X26 X27 X28 X29 X30 X31 X32 X33 X34 X35
## 1 3.5 3.5 2.9 3.2 3.2 2.8 2.6 5.5 3.1 5.2 6.1 6.1 6.1 6.1 5.6 5.2 5.4
## 2 3 2.6 3 2.2 2.3 2.5 2.8 5.5 3.4 15.1 15.3 15.6 15.6 15.9 16.2 16.2 16.2
## 3 4.4 3.5 2.7 2.9 3.9 4.1 4.6 5.6 3.5 16.6 16.7 16.7 16.8 16.8 16.8 16.9 16.9
## 4 2.4 1.9 3.2 4.1 3.9 4.5 4.3 4.7 3.2 18.3 18.2 18.3 18.4 18.6 18.6 18.5 18.7
## 5 3 2.4 2.8 2.5 2.5 3.7 3.4 3.7 2.3 18.8 18.6 18.5 18.5 18.6 18.9 19.2 19.4
## 6 4.4 4.3 3.2 6.2 6.8 5.1 4 6.8 3.2 18.9 19.5 19.6 19.5 19.5 19.5 19.4 19.2
## X36 X37 X38 X39 X40 X41 X42 X43 X44 X45 X46 X47 X48 X49 X50
## 1 7.2 10.6 14.5 17.2 18.3 18.9 19.1 18.9 18.3 17.3 16.8 16.1 15.4 14.9 14.8
## 2 16.6 17.8 19.4 20.6 21.2 21.8 22.4 22.1 20.8 19.1 18.1 17.2 16.5 16.1 16
## 3 17.1 17.6 19.1 21.3 21.8 22 22.1 22.2 21.3 19.8 18.6 18 18 18.2 18.3
## 4 18.6 18.8 19 19 19.3 19.4 19.6 19.2 18.9 18.8 18.6 18.5 18.3 18.5 18.8
## 5 19.8 20.5 21.1 21.9 23.8 25.1 25.8 26 25.6 24.2 22.9 21.6 20 19.5 19.1
## 6 19.1 19.5 19.6 18.6 18.6 18.9 19.2 19.3 19.2 18.8 17.6 16.9 15.6 15.4 15.9
## X51 X52 X53 X54 X55 X56 X57 X58 X59 X60 X61 X62 X63 X64
## 1 15 19.1 12.5 6.7 0.11 3.83 0.14 1612 -2.3 0.3 7.18 0.12 3178.5 -15.5
## 2 16.2 22.4 17.8 9 0.25 -0.41 9.53 1594.5 -2.2 0.96 8.24 7.3 3172 -14.5
## 3 18.4 22.2 18.7 9 0.56 0.89 10.17 1568.5 0.9 0.54 3.8 4.42 3160 -15.9
## 4 18.9 19.6 18.7 9.9 0.89 -0.34 8.58 1546.5 3 0.77 4.17 8.11 3145.5 -16.8
## 5 19.1 26.0 21.1 ? ? ? ? ? ? ? ? ? ? ?
## 6 15.8 19.6 18.5 14.4 0.68 1.52 8.62 1499.5 4.3 0.61 9.04 10.81 3111 -11.8
## X65 X66 X67 X68 X69 X70 X71 X72 X73 X74
## 1 0.15 10.67 -1.56 5795 -12.1 17.9 10330 -55 0.00 0
## 2 0.48 8.39 3.84 5805 14.05 29 10275 -55 0.00 0
## 3 0.6 6.94 9.8 5790 17.9 41.3 10235 -40 0.00 0
## 4 0.49 8.73 10.54 5775 31.15 51.7 10195 -40 2.08 0
## 5 ? ? ? ? ? ? ? ? 0.58 0
## 6 0.09 11.98 11.28 5770 27.95 46.25 10120 ? 5.84 0- Converting the data to numeric data
Assignment_Data <- Assignment_Data %>% mutate_if(is.character,as.numeric)- Reading the TEXT file having list of attribute names of “Assignment_Data”
columnNames <- read_csv("E:/shivani_timeseries/Assignment_columnnames.txt", col_names = FALSE)
columnNames## # A tibble: 74 x 1
## X1
## <chr>
## 1 Date
## 2 WSR0
## 3 WSR1
## 4 WSR2
## 5 WSR3
## 6 WSR4
## 7 WSR5
## 8 WSR6
## 9 WSR7
## 10 WSR8
## # ... with 64 more rows- Assigning column names to Assignment data
colnames(Assignment_Data) <- columnNames$X1
names(Assignment_Data)## [1] "Date" "WSR0" "WSR1" "WSR2" "WSR3" "WSR4" "WSR5" "WSR6"
## [9] "WSR7" "WSR8" "WSR9" "WSR10" "WSR11" "WSR12" "WSR13" "WSR14"
## [17] "WSR15" "WSR16" "WSR17" "WSR18" "WSR19" "WSR20" "WSR21" "WSR22"
## [25] "WSR23" "WSR_PK" "WSR_AV" "T0" "T1" "T2" "T3" "T4"
## [33] "T5" "T6" "T7" "T8" "T9" "T10" "T11" "T12"
## [41] "T13" "T14" "T15" "T16" "T17" "T18" "T19" "T20"
## [49] "T21" "T22" "T23" "T_PK" "T_AV" "T85" "RH85" "U85"
## [57] "V85" "HT85" "T70" "RH70" "U70" "V70" "HT70" "T50"
## [65] "RH50" "U50" "V50" "HT50" "KI" "TT" "SLP" "SLP_"
## [73] "Precp" "Ozone"#structure of the Data
head(Assignment_Data)## Date WSR0 WSR1 WSR2 WSR3 WSR4 WSR5 WSR6 WSR7 WSR8 WSR9 WSR10 WSR11 WSR12
## 1 NA 0.8 1.8 2.4 2.1 2.0 2.1 1.5 1.7 1.9 2.3 3.7 5.5 5.1
## 2 NA 2.8 3.2 3.3 2.7 3.3 3.2 2.9 2.8 3.1 3.4 4.2 4.5 4.5
## 3 NA 2.9 2.8 2.6 2.1 2.2 2.5 2.5 2.7 2.2 2.5 3.1 4.0 4.4
## 4 NA 4.7 3.8 3.7 3.8 2.9 3.1 2.8 2.5 2.4 3.1 3.3 3.1 2.3
## 5 NA 2.6 2.1 1.6 1.4 0.9 1.5 1.2 1.4 1.3 1.4 2.2 2.0 3.0
## 6 NA 3.1 3.5 3.3 2.5 1.6 1.7 1.6 1.6 2.3 1.8 2.5 3.9 3.4
## WSR13 WSR14 WSR15 WSR16 WSR17 WSR18 WSR19 WSR20 WSR21 WSR22 WSR23 WSR_PK
## 1 5.4 5.4 4.7 4.3 3.5 3.5 2.9 3.2 3.2 2.8 2.6 5.5
## 2 4.3 5.5 5.1 3.8 3.0 2.6 3.0 2.2 2.3 2.5 2.8 5.5
## 3 4.6 5.6 5.4 5.2 4.4 3.5 2.7 2.9 3.9 4.1 4.6 5.6
## 4 2.1 2.2 3.8 2.8 2.4 1.9 3.2 4.1 3.9 4.5 4.3 4.7
## 5 3.0 3.1 3.1 2.7 3.0 2.4 2.8 2.5 2.5 3.7 3.4 3.7
## 6 2.7 3.4 2.5 2.2 4.4 4.3 3.2 6.2 6.8 5.1 4.0 6.8
## WSR_AV T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13
## 1 3.1 5.2 6.1 6.1 6.1 6.1 5.6 5.2 5.4 7.2 10.6 14.5 17.2 18.3 18.9
## 2 3.4 15.1 15.3 15.6 15.6 15.9 16.2 16.2 16.2 16.6 17.8 19.4 20.6 21.2 21.8
## 3 3.5 16.6 16.7 16.7 16.8 16.8 16.8 16.9 16.9 17.1 17.6 19.1 21.3 21.8 22.0
## 4 3.2 18.3 18.2 18.3 18.4 18.6 18.6 18.5 18.7 18.6 18.8 19.0 19.0 19.3 19.4
## 5 2.3 18.8 18.6 18.5 18.5 18.6 18.9 19.2 19.4 19.8 20.5 21.1 21.9 23.8 25.1
## 6 3.2 18.9 19.5 19.6 19.5 19.5 19.5 19.4 19.2 19.1 19.5 19.6 18.6 18.6 18.9
## T14 T15 T16 T17 T18 T19 T20 T21 T22 T23 T_PK T_AV T85 RH85 U85
## 1 19.1 18.9 18.3 17.3 16.8 16.1 15.4 14.9 14.8 15.0 19.1 12.5 6.7 0.11 3.83
## 2 22.4 22.1 20.8 19.1 18.1 17.2 16.5 16.1 16.0 16.2 22.4 17.8 9.0 0.25 -0.41
## 3 22.1 22.2 21.3 19.8 18.6 18.0 18.0 18.2 18.3 18.4 22.2 18.7 9.0 0.56 0.89
## 4 19.6 19.2 18.9 18.8 18.6 18.5 18.3 18.5 18.8 18.9 19.6 18.7 9.9 0.89 -0.34
## 5 25.8 26.0 25.6 24.2 22.9 21.6 20.0 19.5 19.1 19.1 26.0 21.1 NA NA NA
## 6 19.2 19.3 19.2 18.8 17.6 16.9 15.6 15.4 15.9 15.8 19.6 18.5 14.4 0.68 1.52
## V85 HT85 T70 RH70 U70 V70 HT70 T50 RH50 U50 V50 HT50 KI
## 1 0.14 1612.0 -2.3 0.30 7.18 0.12 3178.5 -15.5 0.15 10.67 -1.56 5795 -12.10
## 2 9.53 1594.5 -2.2 0.96 8.24 7.30 3172.0 -14.5 0.48 8.39 3.84 5805 14.05
## 3 10.17 1568.5 0.9 0.54 3.80 4.42 3160.0 -15.9 0.60 6.94 9.80 5790 17.90
## 4 8.58 1546.5 3.0 0.77 4.17 8.11 3145.5 -16.8 0.49 8.73 10.54 5775 31.15
## 5 NA NA NA NA NA NA NA NA NA NA NA NA NA
## 6 8.62 1499.5 4.3 0.61 9.04 10.81 3111.0 -11.8 0.09 11.98 11.28 5770 27.95
## TT SLP SLP_ Precp Ozone
## 1 17.90 10330 -55 0.00 0
## 2 29.00 10275 -55 0.00 0
## 3 41.30 10235 -40 0.00 0
## 4 51.70 10195 -40 2.08 0
## 5 NA NA NA 0.58 0
## 6 46.25 10120 NA 5.84 0Visualising the Missing Data
aggr(Assignment_Data[,-c(1)], combined = TRUE, numbers = TRUE)## Warning in plot.aggr(res, ...): not enough vertical space to display frequencies
## (too many combinations)
From the detailed summary of each variable we observes that many attributes have missing data.
Below are the attributes for which we will be forecasting:-
WSR_PK: continuous. peek wind speed – resultant (meaning average of wind vector) T_PK: continuous. Peak T T_AV: continuous. Average T T85: continuous. T at 850 hpa level (or about 1500 m height) RH85: continuous. Relative Humidity at 850 hpa HT85: continuous. Geopotential height at 850 hpa, it is about the same as height at low altitude T70: continuous. T at 700 hpa level (roughly 3100 m height) KI: continuous. K-Index TT: continuous. T-Totals SLP: continuous. Sea level pressure SLP_: continuous. SLP change from previous day
Subselecting the variables to be forecasted from the Assignment_Data and storing it as new dataframe as “ozoneData”
ozoneData <- subset(Assignment_Data,select = c("WSR_PK","T_PK","T_AV","T85","RH85","HT85","T70","KI","TT","SLP","SLP_"))
str(ozoneData)## 'data.frame': 2534 obs. of 11 variables:
## $ WSR_PK: num 5.5 5.5 5.6 4.7 3.7 6.8 7 6.8 4.1 3.3 ...
## $ T_PK : num 19.1 22.4 22.2 19.6 26 19.6 15.8 14.9 17 22.3 ...
## $ T_AV : num 12.5 17.8 18.7 18.7 21.1 18.5 9.7 9 10 16.5 ...
## $ T85 : num 6.7 9 9 9.9 NA 14.4 12.6 3.35 3.9 7.1 ...
## $ RH85 : num 0.11 0.25 0.56 0.89 NA 0.68 0.98 0.73 0.38 0.23 ...
## $ HT85 : num 1612 1594 1568 1546 NA ...
## $ T70 : num -2.3 -2.2 0.9 3 NA 4.3 4.6 -2.45 -1.95 -3 ...
## $ KI : num -12.1 14.1 17.9 31.1 NA ...
## $ TT : num 17.9 29 41.3 51.7 NA ...
## $ SLP : num 10330 10275 10235 10195 NA ...
## $ SLP_ : num -55 -55 -40 -40 NA NA -80 25 55 60 ...#Below displays the detailed summary for each variable of “ozoneData” dataset
summary(ozoneData)## WSR_PK T_PK T_AV T85
## Min. :0.800 Min. : 1.70 Min. : 0.30 Min. :-7.10
## 1st Qu.:3.400 1st Qu.:21.20 1st Qu.:16.00 1st Qu.:10.50
## Median :4.100 Median :26.60 Median :22.20 Median :14.30
## Mean :4.172 Mean :25.58 Mean :20.84 Mean :13.58
## 3rd Qu.:4.800 3rd Qu.:31.10 3rd Qu.:26.80 3rd Qu.:17.40
## Max. :9.600 Max. :41.60 Max. :33.60 Max. :24.50
## NA's :273 NA's :175 NA's :175 NA's :99
## RH85 HT85 T70 KI
## Min. :0.0100 Min. :1351 Min. :-9.900 Min. :-56.700
## 1st Qu.:0.3800 1st Qu.:1512 1st Qu.: 3.500 1st Qu.: -3.575
## Median :0.6400 Median :1535 Median : 6.800 Median : 14.925
## Mean :0.5773 Mean :1531 Mean : 5.931 Mean : 10.511
## 3rd Qu.:0.7900 3rd Qu.:1557 3rd Qu.: 8.800 3rd Qu.: 28.350
## Max. :1.0000 Max. :1642 Max. :16.200 Max. : 42.050
## NA's :105 NA's :95 NA's :107 NA's :136
## TT SLP SLP_
## Min. :-10.10 Min. : 9975 Min. :-135.00
## 1st Qu.: 32.30 1st Qu.:10130 1st Qu.: -20.00
## Median : 41.10 Median :10160 Median : 0.00
## Mean : 37.39 Mean :10164 Mean : -0.12
## 3rd Qu.: 45.10 3rd Qu.:10195 3rd Qu.: 15.00
## Max. : 59.15 Max. :10350 Max. : 140.00
## NA's :125 NA's :95 NA's :158## WSR_PK T_PK T_AV T85 RH85
## nbr.val 2.261000e+03 2.359000e+03 2.359000e+03 2.435000e+03 2.429000e+03
## nbr.null 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## nbr.na 2.730000e+02 1.750000e+02 1.750000e+02 9.900000e+01 1.050000e+02
## min 8.000000e-01 1.700000e+00 3.000000e-01 -7.100000e+00 1.000000e-02
## max 9.600000e+00 4.160000e+01 3.360000e+01 2.450000e+01 1.000000e+00
## range 8.800000e+00 3.990000e+01 3.330000e+01 3.160000e+01 9.900000e-01
## sum 9.433100e+03 6.033930e+04 4.916270e+04 3.305585e+04 1.402310e+03
## median 4.100000e+00 2.660000e+01 2.220000e+01 1.430000e+01 6.400000e-01
## mean 4.172092e+00 2.557834e+01 2.084048e+01 1.357530e+01 5.773199e-01
## SE.mean 2.468278e-02 1.472505e-01 1.443902e-01 9.877082e-02 5.238647e-03
## CI.mean.0.95 4.840328e-02 2.887539e-01 2.831450e-01 1.936836e-01 1.027268e-02
## var 1.377491e+00 5.114950e+01 4.918171e+01 2.375507e+01 6.666007e-02
## std.dev 1.173666e+00 7.151888e+00 7.012967e+00 4.873917e+00 2.581861e-01
## coef.var 2.813134e-01 2.796072e-01 3.365069e-01 3.590284e-01 4.472150e-01
## HT85 T70 KI TT
## nbr.val 2.439000e+03 2.427000e+03 2398.0000000 2409.0000000
## nbr.null 0.000000e+00 1.000000e+00 1.0000000 1.0000000
## nbr.na 9.500000e+01 1.070000e+02 136.0000000 125.0000000
## min 1.351000e+03 -9.900000e+00 -56.7000000 -10.1000000
## max 1.642000e+03 1.620000e+01 42.0500000 59.1500000
## range 2.910000e+02 2.610000e+01 98.7500000 69.2500000
## sum 3.735315e+06 1.439485e+04 25205.5000000 90068.5000000
## median 1.535000e+03 6.800000e+00 14.9250000 41.1000000
## mean 1.531494e+03 5.931129e+00 10.5110509 37.3883354
## SE.mean 7.430115e-01 7.849298e-02 0.4230834 0.2287960
## CI.mean.0.95 1.456999e+00 1.539202e-01 0.8296471 0.4486574
## var 1.346489e+03 1.495311e+01 429.2409375 126.1053477
## std.dev 3.669454e+01 3.866925e+00 20.7181306 11.2296637
## coef.var 2.395996e-02 6.519711e-01 1.9710808 0.3003521
## SLP SLP_
## nbr.val 2.439000e+03 2376.0000000
## nbr.null 0.000000e+00 202.0000000
## nbr.na 9.500000e+01 158.0000000
## min 9.975000e+03 -135.0000000
## max 1.035000e+04 140.0000000
## range 3.750000e+02 275.0000000
## sum 2.479048e+07 -285.0000000
## median 1.016000e+04 0.0000000
## mean 1.016420e+04 -0.1199495
## SE.mean 1.061440e+00 0.7350363
## CI.mean.0.95 2.081418e+00 1.4413792
## var 2.747911e+03 1283.7013955
## std.dev 5.242052e+01 35.8287789
## coef.var 5.157369e-03 -298.6988723OBSERVATION:
Each variable has a large amount of missing data. It could also be noticed that all variables are on differnt scales with respect to each other.
EDA throgh Visualisation Method
#Plotting histogram for each variable
ggplot(gather(ozoneData), aes(value))+geom_histogram(bins = 10)+ facet_wrap(~key,scales='free_x') ## Warning: Removed 1543 rows containing non-finite values (stat_bin).
OBSERVATIONS
1) “SLP”, “SLP_” and “WSR_PK” variables seems to be normally distributed.
2) KI, RH85, T_AV, T_PK, T70 , T85 and TT all these variables are left skewed. Means most of the observations are observed at right side of the graph having larger value compared to left side of the graph.
Plotting boxplots for each variable
OUTLIERS:
boxplot(ozoneData, main = "Boxplot of all variables")
#Boxplot
boxplot(ozoneData[,-c(6,10)], main = "Boxplot of same scale variables")
DEALING WITH OUTLIERS FOR TIME SERIES DATA
An outlier is a point that falls far from the data points. It’s a point that is extreme in some ways. Outliers in a data could be depicted from plotting outliers. The points which lies outside the whisker box are considerd to be outliers.
Here, we see we have many outliers for each variable. However, these datapoint does not seems to be potential outliers as most of the datapoints occurs in bulk.
For time series data, outliers may be errors, or they may simply be unusual. Many time series models are outliers sensitive means they won’t work well if there are extreme outliers in the data.
If the outliers are genuinely errors, then these outliers could be removed easily[1]. However, simply removing outliers could be misleading. This could lead to loss of usefull information which needs to be taken into account while forecasting. Here, we dont notice any extreme outliers for our dataset. So, we are not removing outliers as they dont seem to be potential outliers.
DEALING WITH MISSING VALUES FOR TIME SERIES DATA
#Plot to visualise missing data using “VIM” package,
aggr(ozoneData, numbers = TRUE, prop = c(TRUE, FALSE))
OBSERVATIONs: 1) On total 2090 observations are present in the data without any missing information.
2) Most of the data is missing for WSR_PK comaparitively to other variables.
3) One interesting point could be observed that we have 12 such datapoints which are missing for all variables of “ozoneData”.
There could be four type of Time Series Data:-
- No trend or Seasonality (white noise)
- Has Trend but no Seasonality
- Has Seasonality but No Trend
- Has both Seasonality and Trend
Missing Values of Time Series Data is dealt depending on the type of our time series data.
The R functions for ARIMA models, dynamic regression models and NNAR models will also work correctly without causing errors. However, other modelling functions do not handle missing values including ets(), stlf(), and tbats()[1].
Following are the Time-Series Specific Method for dealing with missing values:
Last Observation Carried Forward (LOCF) & Next Observation Carried Backward (NOCB)
This is a popular statistical approach to analysis of longitudinal repeat measurement data where some follow-up observations may be missing. Longitudinal data tracks the same sample at various points in time. Both methods can introduce bias in analysis and perform poorly when data has a visible trend[2].Linear Interpolation
This method is used for such time series data which has trend but no seasonality.Seasonal Adjustment + Linear Interpolation
This method works best for those time series data which has both trend and seasonality.
#Converting all the variables of ozoneData to time series data such that it starts from the starting month of the year 1998.
tsWSR_PK <- ts(ozoneData$WSR_PK,start = decimal_date(as.Date("1998-01-01")), frequency = 365)
tsT_PK <- ts(ozoneData$T_PK,start = decimal_date(as.Date("1998-01-01")), frequency = 365)
tsT_AV <- ts(ozoneData$T_AV,start = decimal_date(as.Date("1998-01-01")), frequency = 365)
tsT85 <- ts(ozoneData$T85,start = decimal_date(as.Date("1998-01-01")), frequency = 365)
tsRH85 <- ts(ozoneData$RH85, start = decimal_date(as.Date("1998-01-01")), frequency = 365)
tsHT85 <- ts(ozoneData$HT85, start = decimal_date(as.Date("1998-01-01")), frequency = 365)
tsT70 <- ts(ozoneData$T70, start = decimal_date(as.Date("1998-01-01")), frequency = 365)
tsKI <- ts(ozoneData$KI, start = decimal_date(as.Date("1998-01-01")), frequency = 365)
tsTT <- ts(ozoneData$TT, start = decimal_date(as.Date("1998-01-01")), frequency = 365)
tsSLP <- ts(ozoneData$SLP, start = decimal_date(as.Date("1998-01-01")), frequency = 365)
tsSLP_ <- ts(ozoneData$SLP_,start = decimal_date(as.Date("1998-01-01")), frequency = 365)FOR 1st VARIABLE: Forecasting on Peak Wind Speed(WSR_PK)
#Checking the attributes of time series
attributes(tsWSR_PK)## $tsp
## [1] 1998.00 2004.94 365.00
##
## $class
## [1] "ts"#Plotting the series
plot(tsWSR_PK, main = "Peak Wind Speed observed for years (WSR_PK)", ylim = c(0,10), col = "red")
From the plot, we observes that there is no trend but seems to have seasonlity.
Most of the data is missing for year 2002 to 2003 and within year 1998 to 1999 approximately.
Checking the statistics and visualising the missing data in the series:
statsNA(tsWSR_PK)## [1] "Length of time series:"
## [1] 2534
## [1] "-------------------------"
## [1] "Number of Missing Values:"
## [1] 273
## [1] "-------------------------"
## [1] "Percentage of Missing Values:"
## [1] "10.8%"
## [1] "-------------------------"
## [1] "Stats for Bins"
## [1] " Bin 1 (634 values from 1 to 634) : 20 NAs (3.15%)"
## [1] " Bin 2 (634 values from 635 to 1268) : 0 NAs (0%)"
## [1] " Bin 3 (634 values from 1269 to 1902) : 227 NAs (35.8%)"
## [1] " Bin 4 (632 values from 1903 to 2534) : 26 NAs (4.11%)"
## [1] "-------------------------"
## [1] "Longest NA gap (series of consecutive NAs)"
## [1] "183 in a row"
## [1] "-------------------------"
## [1] "Most frequent gap size (series of consecutive NA series)"
## [1] "183 NA in a row (occuring 1 times)"
## [1] "-------------------------"
## [1] "Gap size accounting for most NAs"
## [1] "183 NA in a row (occuring 1 times, making up for overall 183 NAs)"
## [1] "-------------------------"
## [1] "Overview NA series"
## [1] " 7 NA in a row: 1 times"
## [1] " 10 NA in a row: 1 times"
## [1] " 12 NA in a row: 1 times"
## [1] " 15 NA in a row: 1 times"
## [1] " 20 NA in a row: 1 times"
## [1] " 26 NA in a row: 1 times"
## [1] " 183 NA in a row: 1 times"plotNA.distribution(tsWSR_PK)
As we see there is a large gap in the missing data, so locf and NOCB would not seems the good technique to implement here.
Also, as no trend is being observed here, so not necessary to use “Kalman filter with arima state space model” as it works best for series having trend and seasonality.
Hence, using “Linear interpolation” technique to impute missing values. This method works good for series having seasonality but no trend type of time series data.
#Impute the missing values with “na_interpolation” function of “imputeTS package” and visualise the imputed values in the time series
tsWSR_PK.imp <- na_interpolation(tsWSR_PK, method = "linear")
plotNA.imputations(tsWSR_PK, tsWSR_PK.imp)
#Decomposition Of Time Series
decomp <- decompose(tsWSR_PK.imp)
plot(decomp, col = "red")
OBSERVATIONS:
1)There does not seems to have any trend. 2)We observe some seasonality in the series. Means there is some seasonality in the movement of wind speed. Seasonality describes cyclical effects due to the time of the year.
Let’s explore this seasonality pattern by plotting the decomp$seasonal components such that y-axis represents Seasonality Index and x-axis has month
plot(decomp$seasonal[1:365], type ='b', xlab = 'Years', ylab = 'Seasonality Index', col = 'blue', las = 2, main = "SEASONAL DATA")
#las is for numbers to appear verticalOBSERVATIONS:
1) There is 5 - 10% increase in the speed of wind in starting and end months of a year and we could think the reason because of arrival of winter i.e. seasonal change. 2) There is a huge drop of wind speed for mid-months of the year
#Stationarity check of time series
STATIONARY TIME SERIES: It means when there is no change in the mean, variance or co-variance with time within the series. ARIMA models works with stationary series.
Sometimes it is difficult to interpret the series is stationary or not by just looking. So there are some statistical tests which hepls to identify the stationarity of the series.
We could check the stationarity of time series by ADF and KPSS Tests:
- Augmented Dickey- Fuller(ADF) t-statistic test for unit root
The null and alternate hypothesis of this test are:
H0: The series has a unit root(value of a =1)
Ha: The series has no unit root
If we fail to reject the null hypothesis, we can say that the series is non-stationary. This means that the series can be linear or difference stationary[5]
adf.test(tsWSR_PK.imp)## Warning in adf.test(tsWSR_PK.imp): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: tsWSR_PK.imp
## Dickey-Fuller = -6.5322, Lag order = 13, p-value = 0.01
## alternative hypothesis: stationaryNOTE: Here p-value is less, so the series is stationary
- Kwiatkowski-Phillips-Schmidt-Shin (KPSS) for level or trend stationarity
KPSS is another test for checking the stationarity of a time series.The null and alternate hypothesis for the KPSS test are opposite that of the ADF test,
H0: The process is trend stationary
Ha: The series has a unit root(series is not stationary)
kpss.test(tsWSR_PK.imp, null="Trend")## Warning in kpss.test(tsWSR_PK.imp, null = "Trend"): p-value smaller than printed
## p-value##
## KPSS Test for Trend Stationarity
##
## data: tsWSR_PK.imp
## KPSS Trend = 0.62045, Truncation lag parameter = 8, p-value = 0.01NOTE: Here p-value is less, so the series is not stationary.
Following are the possible outcomes:
CASE1: BOTH TESTS RESULTS NOT STATIONARY, THEN SERIES IS NON STATIONARY
CASE2: BOTH TESTS RESULTS STATIONARY, THEN SERIES IS STATIONARY
CASE3: IF KPSS RESULTS STATIONARY AND ADF NOT STATIONARY, MEANS TREND STATIONARY(COULD REMOVE THE TREND TO MAKE IT STATIONARY)
CASE4: IF KPSS RESULTS NOT STATIONARY AND ADF STATIONARY, MEANS DIFFERENCE STATIONARY(COULD USE DIFFERENCING TO MAKE SERIES STATIONARY)
NOTE: From the both tests results, it leads to CASE4, we could recheck by visualising it i.e. by plotting ACF. Second, we can check each for characteristics of stationarity by looking at the autocorrelation functions (ACF) of each signal. For a stationary signal, because we expect no dependence with time, we would expect the ACF to go to 0 for each time lag (τ). Lets visualize the signals and ACFs.
Plotting ACF to check the auto-corelations
acf(tsWSR_PK.imp,lag.max = length(tsWSR_PK.imp),xlab = "lag #", ylab = 'ACF',main='Statiionary Check ')
Here, we observes most of the data lies outside the blue-dotted lines means the significance level. Now, we will take the difference to make our data stationary.
It seems difference of 1 is sufficient to make the series stationary.
tsWSR_PK.sta <- diff(tsWSR_PK.imp)
acf(tsWSR_PK.sta, lag.max = length(tsWSR_PK.sta),xlab = "lag #", ylab = 'ACF',main='Statiionary Check ')
Hence, after differencing our series is now transformed to stationary time series.
#Visualising the stationary series
plot(tsWSR_PK.sta, col = "red")
#CREATING MODELS AND FORECASTING: USING EXPONENTIAL SMOOTHING AND ARIMA TECHNIQUES FOR TIME SERIES FORECASTING
##Exponential Smoothing TECHNIQUE FOR FORECASTING
It is one of the most popular time series technique which uses historical data’s inherent characterstics as input to forecast. The forecasting horizon should be short-term such as the next quarter or potentially six months[5]. There are different exponential smoothing methods that differ from each other in the components of the time series that are modeled[5].
This includes “Simple Exponential Smoothing(ses)”- uses one smoothing constant ,“Holt exponential smoothing(holt)” - uses 2 smoothing constant, “Holt-Winter Exponential Smoothing(hw)”- uses 3 smoothing constant and “Automated exponential smoothing forecasts”.
For “ses” and “Holt exponential smoothing” methods ,the seasonal fluctuations in the data are not part of the model.The method to do so in exponential smoothing is by using “Holt-Winter exponential smoothing”, “Automated exponential smoothing forecasts” methods.
As for “tsWSR_PK.imp” does not have trend but seems to have seasonality, will fit automated exponential smoothening model
##ARIMA TECHNIQUE
ARIMA stands for AUTOREGRESSIVE MOVING AVERAGE MODEL.
a. Auto Regressive (p) - Lags of the variables itself
b. Integrated(d) - Differencing steps required to make stationary
c. Moving Average - Lags of previous information
ARIMA are also renamed as:
AR Model i.e. ARIMA(1,00), MA model i.e. ARIMA(0,0,1) and ARMA model i.e. ARIMA(0,0,1).
ARIMA gives results based on lowest AIC.
#Fit automated exponential smoothing model and ARIMA models to training dataset and calculate forecast accuracy
1.Train - Test Split of the data
train <- window(tsWSR_PK.imp, end = c(2004, 3))
test <- window(tsWSR_PK.imp, start = c(2004, 4))#Model 1 : Auto Exponential Smoothening Model
set.seed(301)
fit_auto_train <- forecast(train)
summary(fit_auto_train)##
## Forecast method: STL + ETS(A,N,N)
##
## Model Information:
## ETS(A,N,N)
##
## Call:
## ets(y = na.interp(x), model = etsmodel, allow.multiplicative.trend = allow.multiplicative.trend)
##
## Smoothing parameters:
## alpha = 0.1273
##
## Initial states:
## l = 4.8892
##
## sigma: 0.8917
##
## AIC AICc BIC
## 16371.83 16371.84 16388.91
##
## Error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -0.004812517 0.8912478 0.6843666 -5.002415 17.82928 0.4926418
## ACF1
## Training set 0.2244226
##
## Forecasts:
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 2004.0082 3.779444 2.6367426562 4.922145 2.031833204 5.527054
## 2004.0110 2.723146 1.5712234928 3.875068 0.961432671 4.484859
## 2004.0137 3.393407 2.2323367772 4.554477 1.617703352 5.169111
## 2004.0164 4.927936 3.7577893676 6.098082 3.138351195 6.717521
## 2004.0192 3.436528 2.2573746637 4.615681 1.633168728 5.239887
## 2004.0219 3.169722 1.9816309000 4.357814 1.352693342 4.986751
## 2004.0247 2.920149 1.7231861814 4.117112 1.089552333 4.750746
## 2004.0274 3.762802 2.5570329718 4.968571 1.918737386 5.606867
## 2004.0301 3.573609 2.3590972927 4.788120 1.716173770 5.431044
## 2004.0329 3.544942 2.3217501589 4.768133 1.674231775 5.415651
## 2004.0356 2.945395 1.7135849988 4.177205 1.061504130 4.829286
## 2004.0384 4.240819 3.0004502531 5.481188 2.343838602 6.137800
## 2004.0411 3.996102 2.7472330098 5.244971 2.086121626 5.906083
## 2004.0438 4.717959 3.4606469679 5.975271 2.795066272 6.640851
## 2004.0466 4.737302 3.4716033233 6.003000 2.801583126 6.673020
## 2004.0493 3.759253 2.4852232698 5.033282 1.810792795 5.707713
## 2004.0521 3.096605 1.8142984563 4.378912 1.135486356 5.057724
## 2004.0548 3.350830 2.0602994403 4.641361 1.377133817 5.324526
## 2004.0575 3.066036 1.7673336063 4.364739 1.079842028 5.052230
## 2004.0603 3.102256 1.7954326157 4.409079 1.103642134 5.100870
## 2004.0630 3.430585 2.1156913098 4.745479 1.419628473 5.441542
## 2004.0658 3.810230 2.4873150531 5.133146 1.787005926 5.833455
## 2004.0685 3.684722 2.3538339018 5.015611 1.649304076 5.720141
## 2004.0712 3.767927 2.4291132473 5.106742 1.720387859 5.815467
## 2004.0740 4.542769 3.1960757464 5.889462 2.483179486 6.602358
## 2004.0767 4.044270 2.6897436837 5.398796 1.972700812 6.115839
## 2004.0795 3.166627 1.8043131668 4.528942 1.083147527 5.250107
## 2004.0822 3.370927 2.0008693368 4.740986 1.275604363 5.466251
## 2004.0849 3.333514 1.9557553009 4.711272 1.226414034 5.440613
## 2004.0877 3.979715 2.5942989533 5.365131 1.860904050 6.098526
## 2004.0904 3.983918 2.5908863977 5.376949 1.853460140 6.114375
## 2004.0932 3.974583 2.5739777451 5.375188 1.832542052 6.116624
## 2004.0959 3.734267 2.3261287365 5.142406 1.580705173 5.887830
## 2004.0986 4.358673 2.9430416558 5.774305 2.193651444 6.523695
## 2004.1014 3.700552 2.2774668011 5.123638 1.524130826 5.876974
## 2004.1041 3.025586 1.5950860172 4.456087 0.837824838 5.213348
## 2004.1068 3.602042 2.1641648744 5.039919 1.402998733 5.801085
## 2004.1096 4.244309 2.7990929321 5.689525 2.034041760 6.454576
## 2004.1123 3.860317 2.4077993346 5.312835 1.638882761 6.081752
## 2004.1151 4.466015 3.0062312219 5.925798 2.233468581 6.698561
## 2004.1178 3.873607 2.4065937986 5.340619 1.630004139 6.117209
## 2004.1205 3.712159 2.2379520352 5.186366 1.457554123 5.966763
## 2004.1233 3.670666 2.1893003366 5.152032 1.405112666 5.936220
## 2004.1260 3.747240 2.2587494555 5.235730 1.470790254 6.023689
## 2004.1288 3.922939 2.4273578199 5.418520 1.635645053 6.210233
## 2004.1315 4.119609 2.6169703520 5.622247 1.821521732 6.417695
## 2004.1342 4.632859 3.1231964053 6.142521 2.324029397 6.941688
## 2004.1370 3.196043 1.6793889779 4.712697 0.876520801 5.515565
## 2004.1397 3.585999 2.0623855278 5.109613 1.255833167 5.916165
## 2004.1425 3.970228 2.4396867329 5.500770 1.629466940 6.310990
## 2004.1452 3.526284 1.9888461093 5.063723 1.174975411 5.877593
## 2004.1479 4.046393 2.5020883043 5.590697 1.684583005 6.408202
## 2004.1507 5.512837 3.9616976546 7.063977 3.140573842 7.885101
## 2004.1534 5.017057 3.4591116276 6.575002 2.634385177 7.399729
## 2004.1562 4.638323 3.0736012619 6.203044 2.245287844 7.031357
## 2004.1589 4.060573 2.4891047720 5.632041 1.657219852 6.463926
## 2004.1616 3.067857 1.4896712230 4.646043 0.654230069 5.481484
## 2004.1644 4.305421 2.7205457433 5.890296 1.881563429 6.729279
## 2004.1671 4.317462 2.7259256421 5.908999 1.883417052 6.751507
## 2004.1699 3.229872 1.6317019472 4.828042 0.785681779 5.674062
## 2004.1726 3.596775 1.9919983829 5.201551 1.142481151 6.051068
## 2004.1753 3.603754 1.9923989939 5.215110 1.139399036 6.068110
## 2004.1781 5.203353 3.5854455322 6.821261 2.728977010 7.677729
## 2004.1808 5.742314 4.1178801074 7.366747 3.257957011 8.226670
## 2004.1836 4.077321 2.4463875541 5.708254 1.583023707 6.571618
## 2004.1863 4.062589 2.4251821780 5.699996 1.558391238 6.566787
## 2004.1890 4.054137 2.4102815684 5.697993 1.540077032 6.568197
## 2004.1918 4.211363 2.5610845647 5.861642 1.687479770 6.735247
## 2004.1945 4.080703 2.4240262215 5.737380 1.547034353 6.614372
## 2004.1973 3.322772 1.6597209188 4.985823 0.779355007 5.866188
## 2004.2000 3.588025 1.9186251706 5.257426 1.034898097 6.141153
## 2004.2027 3.397057 1.7213313133 5.072782 0.834255814 5.959858
## 2004.2055 3.254734 1.5727069336 4.936761 0.682295600 5.827172
## 2004.2082 3.999101 2.3107956301 5.687406 1.417060913 6.581140
## 2004.2110 3.685882 1.9913226011 5.380442 1.094276813 6.277488
## 2004.2137 3.094809 1.3940176465 4.795601 0.493672964 5.695946
## 2004.2164 2.764765 1.0577647258 4.471766 0.154133192 5.375397
## 2004.2192 4.044633 2.3314458499 5.757820 1.424539377 6.664727
## 2004.2219 3.374334 1.6549827941 5.093686 0.744813166 6.003855
## 2004.2247 3.551319 1.8258256667 5.276813 0.912404541 6.190234
## 2004.2274 4.407270 2.6756559579 6.138884 1.758994868 7.055545
## 2004.2301 4.319268 2.5815546970 6.056980 1.661665054 6.976870
## 2004.2329 3.893169 2.1493784254 5.636959 1.226271521 6.560066
## 2004.2356 3.702789 1.9529418731 5.452636 1.026628882 6.378949
## 2004.2384 4.461754 2.7058711994 6.217636 1.776363179 7.147144
## 2004.2411 4.059629 2.2977320729 5.821527 1.365039969 6.754219
## 2004.2438 3.713391 1.9454996713 5.481283 1.009634316 6.417149
## 2004.2466 2.779052 1.0051857139 4.552918 0.066157832 5.491945
## 2004.2493 3.345216 1.5653961932 5.125036 0.623216399 6.067216
## 2004.2521 3.849864 2.0641096315 5.635618 1.118788434 6.580939
## 2004.2548 3.477930 1.6862608504 5.269599 0.737808654 6.218051
## 2004.2575 3.254087 1.4565231501 5.051651 0.504950258 6.003224
## 2004.2603 3.691276 1.8878359855 5.494716 0.933152598 6.449399
## 2004.2630 4.037317 2.2280206269 5.846614 1.270236845 6.804398
## 2004.2658 4.357618 2.5424838605 6.172753 1.581609689 7.133627
## 2004.2685 3.964785 2.1438309881 5.785738 1.179876334 6.749693
## 2004.2712 3.900952 2.0741979499 5.727707 1.107172626 6.694732
## 2004.2740 3.783326 1.9507891987 5.615862 0.980702925 6.585949
## 2004.2767 3.364896 1.5265949780 5.203196 0.553457383 6.176334
## 2004.2795 3.560533 1.7164864364 5.404580 0.740307057 6.380759
## 2004.2822 3.535205 1.6854301510 5.384980 0.706218437 6.364192
## 2004.2849 3.996866 2.1413806336 5.852352 1.159145945 6.834586
## 2004.2877 3.584990 1.7238114578 5.446168 0.738563071 6.431417
## 2004.2904 4.173718 2.3068638917 6.040572 1.318610996 7.028825
## 2004.2932 4.432122 2.5596095426 6.304635 1.568361245 7.295883
## 2004.2959 3.863826 1.9856723948 5.741980 0.991437720 6.736215
## 2004.2986 3.575377 1.6915982567 5.459155 0.694386148 6.456367
## 2004.3014 4.441213 2.5518263600 6.330599 1.551645681 7.330780
## 2004.3041 4.285115 2.3901370821 6.180092 1.386996617 7.183232
## 2004.3068 4.075140 2.1745883000 5.975693 1.168496757 6.981784
## 2004.3096 3.870534 1.9644231496 5.776644 0.955389159 6.785678
## 2004.3123 3.943879 2.0322262913 5.855532 1.020258408 6.867500
## 2004.3151 3.751594 1.8344149347 5.668773 0.819521641 6.683666
## 2004.3178 2.834084 0.9113941378 4.756773 -0.106416159 5.774583
## 2004.3205 3.534298 1.6061140713 5.462482 0.585395109 6.483201
## 2004.3233 3.867054 1.9333912999 5.800717 0.909771936 6.824337
## 2004.3260 3.804647 1.8655205422 5.743774 0.839008972 6.770285
## 2004.3288 2.973231 1.0286564533 4.917806 -0.000739197 5.947201
## 2004.3315 2.796357 0.8463489544 4.746364 -0.185922718 5.778636
## 2004.3342 3.458482 1.5030561937 5.413907 0.467916489 6.449047
## 2004.3370 3.539810 1.5789813686 5.500638 0.540981557 6.538638
## 2004.3397 4.363802 2.3975861060 6.330019 1.356734046 7.370871
## 2004.3425 3.758230 1.7866401390 5.729819 0.742943626 6.773516
## 2004.3452 3.127244 1.1502955339 5.104192 0.103762298 6.150725
## 2004.3479 2.907374 0.9250815456 4.889667 -0.124280744 5.939029
## 2004.3507 3.905534 1.9179116375 5.893156 0.865727901 6.945340
## 2004.3534 3.628857 1.6359193778 5.621795 0.580921739 6.676793
## 2004.3562 3.599975 1.6017358440 5.598215 0.543931789 6.656019
## 2004.3589 3.759797 1.7562703617 5.763324 0.695667316 6.823927
## 2004.3616 3.254322 1.2455216705 5.263122 0.182127002 6.326517
## 2004.3644 3.533048 1.5189882523 5.547108 0.452809270 6.613287
## 2004.3671 3.389051 1.3697453207 5.408357 0.300789277 6.477313
## 2004.3699 3.453453 1.4289142415 5.477991 0.357188332 6.549717
## 2004.3726 2.461124 0.4313663949 4.490881 -0.643122240 5.565370
## 2004.3753 3.253690 1.2187270821 5.288653 0.141482807 6.365897
## 2004.3781 3.161180 1.1210245026 5.201335 0.041031619 6.281328
## 2004.3808 2.947613 0.9022788353 4.992947 -0.180455680 6.075682
## 2004.3836 3.285723 1.2352229798 5.336223 0.149753758 6.421693
## 2004.3863 3.622941 1.5672876108 5.678594 0.479090554 6.766791
## 2004.3890 3.678382 1.6175883664 5.739175 0.526670297 6.830093
## 2004.3918 3.070614 1.0046929152 5.136534 -0.088939398 6.230166
## 2004.3945 3.293574 1.2225390411 5.364610 0.126199204 6.460949
## 2004.3973 3.300423 1.2242857037 5.376560 0.125245013 6.475601
## 2004.4000 3.755199 1.6739720153 5.836426 0.572237092 6.938161
## 2004.4027 3.529622 1.4433180204 5.615926 0.338895438 6.720348
## 2004.4055 2.987846 0.8964772658 5.079215 -0.210626452 6.186318
## 2004.4082 2.847565 0.7511432617 4.943986 -0.358635114 6.053764
## 2004.4110 2.973952 0.8724899323 5.075413 -0.239956671 6.187860
## 2004.4137 3.396945 1.2904550652 5.503435 0.175346619 6.618544
## 2004.4164 3.526150 1.4146438609 5.637657 0.296879911 6.755421
## 2004.4192 3.086001 0.9694900075 5.202512 -0.150923153 6.322925
## 2004.4219 3.110623 0.9891195415 5.232127 -0.133936580 6.355183
## 2004.4247 2.457786 0.3313012370 4.584270 -0.794391640 5.709963
## 2004.4274 2.625129 0.4936750222 4.756583 -0.634648448 5.884906
## 2004.4301 2.943813 0.8074012442 5.080224 -0.323546701 6.211172
## 2004.4329 2.469123 0.3277651604 4.610481 -0.805801184 5.744047
## 2004.4356 2.449614 0.3033214405 4.595907 -0.832857268 5.732085
## 2004.4384 2.973090 0.8218738272 5.124306 -0.316911253 6.263091
## 2004.4411 2.703488 0.5473592737 4.859616 -0.594026227 6.001002
## 2004.4438 2.572985 0.4119551201 4.734014 -0.732024889 5.877994
## 2004.4466 2.819954 0.6540347560 4.985874 -0.492533892 6.132443
## 2004.4493 2.973583 0.8027844426 5.144382 -0.346367012 6.293533
## 2004.4521 3.077371 0.9017037201 5.253037 -0.250024749 6.404766
## 2004.4548 2.912194 0.7316698747 5.092718 -0.422629856 6.247018
## 2004.4575 3.009123 0.8237527349 5.194494 -0.333112542 6.351359
## 2004.4603 3.075898 0.8856919595 5.266104 -0.273733187 6.425530
## 2004.4630 3.384883 1.1898513985 5.579914 0.027872022 6.741893
## 2004.4658 3.143759 0.9439135509 5.343605 -0.220614453 6.508133
## 2004.4685 2.772826 0.5681760331 4.977475 -0.598895033 6.144547
## 2004.4712 3.111874 0.9024311661 5.321318 -0.267177433 6.490926
## 2004.4740 3.144519 0.9302927683 5.358746 -0.241847870 6.530886
## 2004.4767 3.527727 1.3087273093 5.746726 0.134060089 6.921393
## 2004.4795 3.293097 1.0693353337 5.516859 -0.107853045 6.694047
## 2004.4822 2.743152 0.5146374653 4.971666 -0.665066685 6.151370
## 2004.4849 2.983511 0.7502546910 5.216768 -0.431959876 6.398982
## 2004.4877 3.031971 0.7939824901 5.269960 -0.390737175 6.454680
## 2004.4904 3.146489 0.9037776685 5.389200 -0.283441808 6.576419
## 2004.4932 2.952027 0.7046033063 5.199450 -0.485110729 6.389164
## 2004.4959 3.394896 1.1427699759 5.647022 -0.049433399 6.839225
## 2004.4986 3.195302 0.9384833518 5.452120 -0.256204176 6.646808
## 2004.5014 3.141474 0.8799723573 5.402975 -0.317194169 6.600142
## 2004.5041 2.923191 0.6570166136 5.189366 -0.542623788 6.389006
## 2004.5068 3.155422 0.8845838318 5.426260 -0.317525353 6.628370
## 2004.5096 3.016617 0.7411243823 5.292109 -0.463448527 6.496682
## 2004.5123 2.792930 0.5127932231 5.073067 -0.694238382 6.280099
## 2004.5151 3.156801 0.8720286096 5.441573 -0.337456693 6.651058
## 2004.5178 3.072207 0.7828094760 5.361605 -0.429124556 6.573539
## 2004.5205 3.031100 0.7370853644 5.325114 -0.477292460 6.539492
## 2004.5233 3.339231 1.0406096226 5.637853 -0.176207086 6.854669
## 2004.5260 3.010581 0.7073611526 5.313800 -0.511889561 6.533051
## 2004.5288 3.358299 1.0504908914 5.666107 -0.171188978 6.887787
## 2004.5315 2.798293 0.4859055799 5.110681 -0.738198626 6.334786
## 2004.5342 3.084867 0.7679086575 5.401826 -0.458615092 6.628349
## 2004.5370 3.279240 0.9577198623 5.600760 -0.271218667 6.829699
## 2004.5397 3.505831 1.1797585684 5.831904 -0.051590005 7.063253
## 2004.5425 3.148788 0.8181713964 5.479405 -0.415582514 6.713159
## 2004.5452 3.648061 1.3129093643 5.983212 0.076754798 7.219367
## 2004.5479 3.047522 0.7078439413 5.387199 -0.530706628 6.625750
## 2004.5507 3.415722 1.0715271553 5.759917 -0.169414791 7.000859
## 2004.5534 3.036535 0.6878315540 5.385239 -0.555497170 6.628568
## 2004.5562 2.952802 0.5995979728 5.306006 -0.646112956 6.551717
## 2004.5589 3.228395 0.8706997740 5.586091 -0.377388812 6.834179
## 2004.5616 3.511464 1.1492860143 5.873643 -0.101175709 7.124105
## 2004.5644 3.180136 0.8134827281 5.546789 -0.439347636 6.799619
## 2004.5671 2.898319 0.5272005332 5.269438 -0.727994003 6.524633
## 2004.5699 3.356230 0.9806537295 5.731807 -0.276900534 6.989361
## 2004.5726 3.154182 0.7741557806 5.534207 -0.485753790 6.794117
## 2004.5753 3.758840 1.3743732732 6.143307 0.112112790 7.405567
## 2004.5781 3.228186 0.8392868664 5.617086 -0.425320159 6.881693
## 2004.5808 3.349316 0.9559914660 5.742640 -0.310957756 7.009589
## 2004.5836 3.264179 0.8664382604 5.661919 -0.402848835 6.931206
## 2004.5863 3.044852 0.6427029905 5.447000 -0.628917681 6.718621
## 2004.5890 3.034840 0.6282909517 5.441389 -0.645659022 6.715338
## 2004.5918 3.281519 0.8705781386 5.692460 -0.405696885 6.968735
## 2004.5945 2.987035 0.5717095653 5.402360 -0.706886281 6.680956
## 2004.5973 3.097615 0.6779141966 5.517317 -0.602998267 6.798229
## 2004.6000 3.784652 1.3605821573 6.208721 0.077357259 7.491946
## 2004.6027 4.038829 1.6103986285 6.467259 0.324865455 7.752792
## 2004.6055 3.444853 1.0120701738 5.877635 -0.275767138 7.165473
## 2004.6082 2.776498 0.3393707351 5.213626 -0.950766600 6.503763
## 2004.6110 2.948794 0.5073291909 5.390258 -0.785104074 6.682692
## 2004.6137 3.579169 1.1333748328 6.024963 -0.161350291 7.319688
## 2004.6164 3.220736 0.7706198204 5.670851 -0.526393112 6.967864
## 2004.6192 3.293723 0.8392934278 5.748153 -0.460003286 7.047450
## 2004.6219 3.004188 0.5454518139 5.462925 -0.756124673 6.764501
## 2004.6247 2.895269 0.4322332359 5.358304 -0.871619038 6.662157
## 2004.6274 2.825361 0.3580340285 5.292688 -0.948090067 6.598812
## 2004.6301 2.892591 0.4209797326 5.364202 -0.887412240 6.672594
## 2004.6329 3.508446 1.0325583677 5.984334 -0.278097558 7.294990
## 2004.6356 3.325353 0.8451952605 5.805510 -0.467720715 7.118426
## 2004.6384 3.523310 1.0388905324 6.007729 -0.276281608 7.322901
## 2004.6411 2.868934 0.3802603050 5.357608 -0.937164137 6.675033
## 2004.6438 3.259458 0.7665365654 5.752379 -0.553136334 7.072052
## 2004.6466 3.031638 0.5344760691 5.528799 -0.787441463 6.850717
## 2004.6493 3.793565 1.2921700849 6.294959 -0.031988276 7.619118
## 2004.6521 3.725934 1.2203136542 6.231555 -0.106081749 7.557950
## 2004.6548 3.205093 0.6952541312 5.714933 -0.633374548 7.043561
## 2004.6575 2.863936 0.3498850472 5.377987 -0.980973160 6.708845
## 2004.6603 3.304459 0.7862033912 5.822715 -0.546880616 7.155799
## 2004.6630 3.155843 0.6333893566 5.678296 -0.701916740 7.013602
## 2004.6658 2.840049 0.3134052296 5.366693 -1.024119265 6.704218
## 2004.6685 2.707848 0.1770203929 5.238676 -1.162718826 6.578415
## 2004.6712 2.795132 0.2601271291 5.330136 -1.081823159 6.672086
## 2004.6740 3.059165 0.5199909848 5.598340 -0.824166735 6.942497
## 2004.6767 3.324944 0.7816068707 5.868282 -0.564754662 7.214643
## 2004.6795 3.290368 0.7428738288 5.837861 -0.605687916 7.186423
## 2004.6822 3.332360 0.7807163302 5.884003 -0.570042042 7.234761
## 2004.6849 3.567930 1.0121439576 6.123716 -0.340807476 7.476668
## 2004.6877 3.691913 1.1319909281 6.251835 -0.223150018 7.606976
## 2004.6904 3.241411 0.6773589460 5.805462 -0.679967980 7.162789
## 2004.6932 3.113256 0.5450816813 5.681430 -0.814427710 7.040940
## 2004.6959 3.496012 0.9237209994 6.068302 -0.437967360 7.429990
## 2004.6986 3.445482 0.8690818196 6.021882 -0.494782026 7.385746
## 2004.7014 3.180317 0.5998143100 5.760821 -0.766221557 7.126857
## 2004.7041 2.915929 0.3313289386 5.500528 -1.036875502 6.868733
## 2004.7068 2.697170 0.1084802211 5.285860 -1.261889361 6.656229
## 2004.7096 3.285659 0.6928852788 5.878432 -0.679646030 7.250963
## 2004.7123 2.625101 0.0282504506 5.221952 -1.346439186 6.596641
## 2004.7151 2.654321 0.0533995975 5.255242 -1.323444982 6.632087
## 2004.7178 3.179420 0.5744341220 5.784406 -0.804562034 7.163402
## 2004.7205 3.334191 0.7251466940 5.943234 -0.655997687 7.324379
## 2004.7233 3.125878 0.5127826834 5.738974 -0.870506585 7.122263
## 2004.7260 3.821928 1.2047870054 6.439069 -0.180643831 7.824500
## 2004.7288 3.536404 0.9152232503 6.157584 -0.472345848 7.545153
## 2004.7315 3.239520 0.6143067982 5.864734 -0.775397273 7.254438
## 2004.7342 3.905553 1.2763123173 6.534793 -0.115523451 7.926629
## 2004.7370 3.479877 0.8466158018 6.113138 -0.547348404 7.507102
## 2004.7397 3.201934 0.5646580433 5.839209 -0.831431355 7.235299
## 2004.7425 3.228888 0.5876042268 5.870172 -0.810607134 7.268384
## 2004.7452 3.152221 0.5069346958 5.797508 -0.893395412 7.197838
## 2004.7479 3.900346 1.2510634652 6.549629 -0.151382189 7.952075
## 2004.7507 2.944691 0.2914182425 5.597965 -1.113139772 7.002523
## 2004.7534 3.673922 1.0166642118 6.331179 -0.390002990 7.737847
## 2004.7562 3.847909 1.1866725359 6.509145 -0.222100696 7.917918
## 2004.7589 3.778530 1.1133214704 6.443738 -0.297554647 7.854614
## 2004.7616 3.115121 0.4459457552 5.784296 -0.967030119 7.197272
## 2004.7644 3.357914 0.6847779628 6.031049 -0.730294552 7.446122
## 2004.7671 3.465230 0.7881391945 6.142320 -0.629026859 7.559486
## 2004.7699 3.754470 1.0734310867 6.435510 -0.345825417 7.854766
## 2004.7726 3.840091 1.1551088022 6.525074 -0.266235078 7.946418
## 2004.7753 3.983698 1.2947778317 6.672618 -0.128650364 8.096046
## 2004.7781 3.932843 1.2399918318 6.625695 -0.185517631 8.051204
## 2004.7808 3.782285 1.0855072066 6.479062 -0.342080489 7.906650
## 2004.7836 3.325113 0.6244155310 6.025811 -0.805247377 7.455473
## 2004.7863 3.301687 0.5970749860 6.006299 -0.834660127 7.438034
## 2004.7890 3.602056 0.8935351018 6.310577 -0.540269220 7.744381
## 2004.7918 3.280751 0.5683268458 5.993175 -0.867543704 7.429045
## 2004.7945 3.376233 0.6599113569 6.092555 -0.778022451 7.530488
## 2004.7973 3.557491 0.8372772956 6.277705 -0.602716815 7.717699
## 2004.8000 4.054772 1.3306723675 6.778873 -0.111379101 8.220924
## 2004.8027 3.839486 1.1115048373 6.567467 -0.332601059 8.011573
## 2004.8055 3.100940 0.3690832557 5.832796 -1.077074150 7.278953
## 2004.8082 3.573701 0.8379752093 6.309428 -0.610230799 7.757634
## 2004.8110 3.822717 1.0831267023 6.562308 -0.367125015 8.012560
## 2004.8137 3.463569 0.7201188224 6.207018 -0.732175723 7.659313
## 2004.8164 3.313529 0.5662260416 6.060833 -0.888108462 7.515167
## 2004.8192 3.821311 1.0701599748 6.572463 -0.386211629 8.028834
## 2004.8219 3.742743 0.9877485046 6.497737 -0.470657355 7.956143
## 2004.8247 2.114504 -0.6443278758 4.873336 -2.104765157 6.333773
## 2004.8274 2.346998 -0.4156655234 5.109662 -1.878131404 6.572128
## 2004.8301 3.099915 0.3334241487 5.866405 -1.131067522 7.330897
## 2004.8329 3.050182 0.2798695437 5.820494 -1.186645119 7.287008
## 2004.8356 2.909701 0.1355722291 5.683829 -1.332962638 7.152364
## 2004.8384 3.267784 0.4898447090 6.045724 -0.980707588 7.516276
## 2004.8411 3.446398 0.6646531523 6.228144 -0.807913810 7.700711
## 2004.8438 3.057415 0.2718689195 5.842961 -1.202709956 7.317539
## 2004.8466 3.523398 0.7340571754 6.312740 -0.742530872 7.789328
## 2004.8493 3.797508 1.0043767907 6.590640 -0.474217699 8.069234
## 2004.8521 2.847015 0.0500987063 5.643932 -1.430499506 7.124530
## 2004.8548 2.991343 0.1906466606 5.792040 -1.291952566 7.274639
## 2004.8575 3.716269 0.9117972741 6.520740 -0.572800270 8.005338
## 2004.8603 3.934839 1.1265980524 6.743081 -0.359995123 8.229674
## 2004.8630 4.406596 1.5945897378 7.218602 0.106003606 8.707188
## 2004.8658 3.526536 0.7107702500 6.342302 -0.779806173 7.832878
## 2004.8685 3.837702 1.0181817500 6.657223 -0.474382310 8.149787
## 2004.8712 3.596493 0.7732226729 6.419763 -0.721326381 7.914312
## 2004.8740 3.857116 1.0301005999 6.684131 -0.466430815 8.180662
## 2004.8767 3.906089 1.0753337886 6.736844 -0.423177365 8.235355
## 2004.8795 3.270415 0.4359252556 6.104905 -1.064563025 7.605393
## 2004.8822 3.333994 0.4957740387 6.172214 -1.006688766 7.674676
## 2004.8849 4.122678 1.2807326866 6.964622 -0.223702052 8.469057
## 2004.8877 3.804409 0.9587441315 6.650074 -0.547659959 8.156478
## 2004.8904 3.789673 0.9402920990 6.639053 -0.568078772 8.147424
## 2004.8932 3.714606 0.8615146206 6.567696 -0.648820470 8.078032
## 2004.8959 3.560560 0.7037633421 6.417357 -0.808533417 7.929653
## 2004.8986 3.547938 0.6874401529 6.408435 -0.826815733 7.922691
## 2004.9014 3.972143 1.1079492331 6.836336 -0.408263249 8.352549
## 2004.9041 3.755462 0.8875766849 6.623346 -0.630589871 8.141513
## 2004.9068 3.448248 0.5766761459 6.319819 -0.943441972 7.839937
## 2004.9096 4.557044 1.6817906266 7.432297 0.159723449 8.954364
## 2004.9123 5.271880 2.3929499772 8.150811 0.868936232 9.674825
## 2004.9151 5.449443 2.5668396621 8.332046 1.040881833 9.858003
## 2004.9178 3.386854 0.5005829314 6.273124 -1.027316508 7.801024
## 2004.9205 4.479393 1.5894595555 7.369327 0.059620969 8.899166
## 2004.9233 4.873154 1.9795617551 7.766747 0.447786478 9.298522
## 2004.9260 4.640047 1.7428006941 7.537293 0.209091171 9.071003
## 2004.9288 4.375590 1.4746941990 7.276485 -0.060947134 8.812127
## 2004.9315 5.339619 2.4350786024 8.244159 0.897507887 9.781730
## 2004.9342 3.647156 0.7389759607 6.555337 -0.800521719 8.094834
## 2004.9370 3.993534 1.0817176323 6.905349 -0.459704603 8.446772
## 2004.9397 3.401641 0.4861940319 6.317088 -1.057150359 7.860432
## 2004.9425 3.873255 0.9541818322 6.792329 -0.591082323 8.337593
## 2004.9452 3.798746 0.8760506721 6.721442 -0.671130866 8.268623
## 2004.9479 4.834415 1.9081018351 7.760728 0.359005288 9.309824
## 2004.9507 4.485037 1.5551104645 7.414963 0.004101272 8.965972
## 2004.9534 4.628231 1.6946967644 7.561766 0.141777283 9.114686
## 2004.9562 3.974883 1.0377441651 6.912022 -0.517083259 8.466849
## 2004.9589 3.930952 0.9902133642 6.871691 -0.566519663 8.428424
## 2004.9616 4.343130 1.3987960029 7.287464 -0.159840298 8.846100
## 2004.9644 3.899447 0.9515223998 6.847372 -0.609014854 8.407910
## 2004.9671 4.009766 1.0582541754 6.961277 -0.504181718 8.523713
## 2004.9699 4.319703 1.3646093353 7.274797 -0.199722894 8.839129
## 2004.9726 3.333536 0.3748644480 6.292208 -1.191361821 7.858434
## 2004.9753 4.017467 1.0552211304 6.979712 -0.512896890 8.547830
## 2004.9781 4.172191 1.2063765619 7.138006 -0.363630931 8.708014
## 2004.9808 4.346757 1.3773775461 7.316137 -0.194517148 8.888032
## 2004.9836 4.706885 1.7339449938 7.679826 0.160165362 9.253606
## 2004.9863 4.760269 1.7837723662 7.736766 0.208110051 9.312429
## 2004.9890 4.496551 1.5165017390 7.476600 -0.061041013 9.054143
## 2004.9918 4.115070 1.1314726990 7.098667 -0.447948250 8.678088
## 2004.9945 3.541175 0.5540336589 6.528316 -1.027263257 8.109613
## 2004.9973 3.419677 0.4289965089 6.410358 -1.154174151 7.993528
## 2005.0000 3.636529 0.6423130922 6.630745 -0.942729096 8.215787
## 2005.0027 4.057684 1.0599370890 7.055431 -0.526974421 8.642343
## 2005.0055 4.086440 1.0851654886 7.087714 -0.503613143 8.676493
## 2005.0082 3.779444 0.7746465962 6.784241 -0.815996966 8.374885
## 2005.0110 2.723146 -0.2851702519 5.731462 -1.877676561 7.323968
## 2005.0137 3.393407 0.3815762278 6.405238 -1.212790651 7.999605
## 2005.0164 4.927936 1.9125945966 7.943277 0.316369316 9.539503
## 2005.0192 3.436528 0.4176798913 6.455376 -1.180401630 8.053457
## 2005.0219 3.169722 0.1473719210 6.192073 -1.452563687 7.792008
## 2005.0247 2.920149 -0.1056996939 5.945998 -1.707487243 7.547785
## 2005.0274 3.762802 0.7334589694 6.792145 -0.870178381 8.395782
## 2005.0301 3.573609 0.5407753384 6.606442 -1.064709683 8.211927
## 2005.0329 3.544942 0.5086217832 6.581261 -1.098708785 8.188592
## 2005.0356 2.945395 -0.0944069611 5.985197 -1.703580959 7.594371
## 2005.0384 4.240819 1.1975388077 7.284100 -0.413476511 8.895115
## 2005.0411 3.996102 0.9493473951 7.042857 -0.663507142 8.655711
## 2005.0438 4.717959 1.6677336762 7.768184 0.053042015 9.382876
## 2005.0466 4.737302 1.6836099833 7.790993 0.067083286 9.407520
## 2005.0493 3.759253 0.7020986089 6.816407 -0.916261043 8.434767
## 2005.0521 3.096605 0.0359922645 6.157218 -1.584198269 7.777408
## 2005.0548 3.350830 0.2867625358 6.414898 -1.335256812 8.036917
## 2005.0575 3.066036 -0.0014821972 6.133554 -1.625328301 7.757401
## 2005.0603 3.102256 0.0312906905 6.173221 -1.594380115 7.798892
## 2005.0630 3.430585 0.3561769740 6.504994 -1.271316488 8.132487
## 2005.0658 3.810230 0.7323829229 6.888078 -0.896931157 8.517392
## 2005.0685 3.684722 0.6034394706 6.766005 -1.027693195 8.397138
## 2005.0712 3.767927 0.6832128594 6.852642 -0.949736367 8.485591
## 2005.0740 4.542769 1.4546265716 7.630911 -0.180137196 9.265675
## 2005.0767 4.044270 0.9527036934 7.135836 -0.683872604 8.772412
## 2005.0795 3.166627 0.0716411100 6.261614 -1.566745712 7.900001
## 2005.0822 3.370927 0.2725247180 6.469330 -1.367670630 8.109526
## 2005.0849 3.333514 0.2316983588 6.435329 -1.410303523 8.077331
## 2005.0877 3.979715 0.8744906399 7.084939 -0.769315791 8.728746
## 2005.0904 3.983918 0.8752883584 7.092547 -0.770320643 8.738156
## 2005.0932 3.974583 0.8625522996 7.086614 -0.784857299 8.734024
## 2005.0959 3.734267 0.6188388605 6.849696 -1.030369370 8.498904
## 2005.0986 4.358673 1.2398509632 7.477496 -0.411153939 9.128501
## 2005.1014 3.700552 0.5783395269 6.822765 -1.074460095 8.475565
## 2005.1041 3.025586 -0.1000129987 6.151186 -1.754605393 7.805778
## 2005.1068 3.602042 0.4730595454 6.731024 -1.183323681 8.387408
## 2005.1096 4.244309 1.1119472924 7.376671 -0.546224832 9.034843
## 2005.1123 3.860317 0.7245799454 6.996055 -0.935379149 8.656014
## 2005.1151 4.466015 1.3269051891 7.605124 -0.334838954 9.266868
## 2005.1178 3.873607 0.7311287592 7.016084 -0.932398517 8.679612
## 2005.1205 3.712159 0.5663161436 6.858001 -1.098992356 8.523310
## 2005.1233 3.670666 0.5214622525 6.819870 -1.145625568 8.486958
## 2005.1260 3.747240 0.5946783310 6.899801 -1.074186913 8.568667
## 2005.1288 3.922939 0.7670232877 7.078854 -0.903617488 8.749495
## 2005.1315 4.119609 0.9603425139 7.278875 -0.712071910 8.951289
## 2005.1342 4.632859 1.4702458213 7.795472 -0.203940371 9.469658
## 2005.1370 3.196043 0.0300866546 6.361999 -1.645869433 8.037956
## 2005.1397 3.585999 0.4167029089 6.755296 -1.261021207 8.433020
## 2005.1425 3.970228 0.7975956883 7.142861 -0.881894594 8.822351
## 2005.1452 3.526284 0.3503189258 6.702250 -1.330935669 8.383505
## 2005.1479 4.046393 0.8670976760 7.225687 -0.815919381 8.908705
## 2005.1507 5.512837 2.3302166734 8.695458 0.645438999 10.380236
## 2005.1534 5.017057 1.8311137747 8.203000 0.144577319 9.889537
## 2005.1562 4.638323 1.4490603990 7.827585 -0.239233005 9.515878
## 2005.1589 4.060573 0.8679951327 7.253150 -0.822053393 8.943199
## 2005.1616 3.067857 -0.1280325950 6.263747 -1.819834421 7.955549
## 2005.1644 4.305421 1.1062227004 7.504619 -0.587330612 9.198173
## 2005.1671 4.317462 1.1149586764 7.519966 -0.580344312 9.215269
## 2005.1699 3.229872 0.0240667018 6.435677 -1.672984159 8.132728
## 2005.1726 3.596775 0.3876708349 6.805878 -1.311126100 8.504675
## 2005.1753 3.603754 0.3913554469 6.816153 -1.309185769 8.516694
## 2005.1781 5.203353 1.9876626101 8.419044 0.285378901 10.121327
## 2005.1808 5.742314 2.5233347471 8.961292 0.819310326 10.665317
## 2005.1836 4.077321 0.8550569997 7.299584 -0.850706357 9.005348
## 2005.1863 4.062589 0.8370439742 7.288135 -0.870456547 8.995635
## 2005.1890 4.054137 0.8253135547 7.282961 -0.883922366 8.992197
## 2005.1918 4.211363 0.9792648691 7.443462 -0.731704691 9.154431
## 2005.1945 4.080703 0.8453332551 7.316073 -0.867368189 9.028775
## 2005.1973 3.322772 0.0841333699 6.561410 -1.630298209 8.275842
## 2005.2000 3.588025 0.3461219998 6.829929 -1.370037969 8.546089
## 2005.2027 3.397057 0.1518917476 6.642222 -1.565994873 8.360109
## 2005.2055 3.254734 0.0063104616 6.503158 -1.713301076 8.222769
## 2005.2082 3.999101 0.7474219970 7.250779 -0.973912730 8.972114
## 2005.2110 3.685882 0.4309518036 6.940813 -1.292104389 8.663869
## 2005.2137 3.094809 -0.1633700719 6.352989 -1.888146013 8.077764
## 2005.2164 2.764765 -0.4966594277 6.026190 -2.223153403 7.752684
## 2005.2192 4.044633 0.7799659848 7.309300 -0.948244317 9.037510
## 2005.2219 3.374334 0.1064281744 6.642240 -1.623496752 8.372165
## 2005.2247 3.551319 0.2801774781 6.822461 -1.451460374 8.554099
## 2005.2274 4.407270 1.1328956110 7.681644 -0.600453475 9.414993
## 2005.2301 4.319268 1.0416638232 7.596871 -0.693394808 9.331930
## 2005.2329 3.893169 0.6123388729 7.173999 -1.124427621 8.910765
## 2005.2356 3.702789 0.4187357030 6.986842 -1.319736976 8.725315
## 2005.2384 4.461754 1.1744806819 7.749027 -0.565696510 9.489204
## 2005.2411 4.059629 0.7691396835 7.350119 -0.972740352 9.091999
## 2005.2438 3.713391 0.4196880873 7.007095 -1.323893130 8.750676
## 2005.2466 2.779052 -0.5178621889 6.075965 -2.263142929 7.821246
## 2005.2493 3.345216 0.0450950419 6.645337 -1.701883568 8.392316
## 2005.2521 3.849864 0.5465384938 7.153189 -1.202136337 8.901864
## 2005.2548 3.477930 0.1714031764 6.784456 -1.578966232 8.534826
## 2005.2575 3.254087 -0.0556374250 6.563812 -1.807699772 8.315874
## 2005.2603 3.691276 0.3783563263 7.004195 -1.375397325 8.757949
## 2005.2630 4.037317 0.7212058795 7.353429 -1.034237446 9.108872
## 2005.2658 4.357618 1.0383181967 7.676919 -0.718813179 9.434050
## 2005.2685 3.964785 0.6422987525 7.287271 -1.116519053 9.046088
## 2005.2712 3.900952 0.5752836571 7.226621 -1.185218963 8.987124
## 2005.2740 3.783326 0.4544775307 7.112174 -1.307708292 8.874360
## 2005.2767 3.364896 0.0328707813 6.696921 -1.730996639 8.460788
## 2005.2795 3.560533 0.2253347194 6.895732 -1.540212697 8.661279
## 2005.2822 3.535205 0.1968360814 6.873574 -1.570389733 8.640800
## 2005.2849 3.996866 0.6553295358 7.338403 -1.113573085 9.107305
## 2005.2877 3.584990 0.2402888104 6.929691 -1.530289028 8.700269
## 2005.2904 4.173718 0.8258553252 7.521581 -0.946396148 9.293832
## 2005.2932 4.432122 1.0811008366 7.783143 -0.692822692 9.557067
## 2005.2959 3.863826 0.5096494763 7.218003 -1.265944533 8.993597
## 2005.2986 3.575377 0.2180471974 6.932706 -1.559215723 8.709969
## 2005.3014 4.441213 1.0807333740 7.801692 -0.698196891 9.580622
## 2005.3041 4.285115 0.9214885239 7.648741 -0.859107525 9.429337
## 2005.3068 4.075140 0.7083706623 7.441910 -1.073889614 9.224171
## 2005.3096 3.870534 0.5006230612 7.240444 -1.283299889 9.024367
## 2005.3123 3.943879 0.5708305150 7.316928 -1.214753562 9.102512
## 2005.3151 3.751594 0.3754103653 7.127778 -1.411833293 8.915021
## 2005.3178 2.834084 -0.5452321999 6.213399 -2.334133901 8.002301
## 2005.3205 3.534298 0.1518531184 6.916743 -1.638705090 8.707301
## 2005.3233 3.867054 0.4814830109 7.252626 -1.310730174 9.044839
## 2005.3260 3.804647 0.4159523205 7.193342 -1.377914314 8.987208
## 2005.3288 2.973231 -0.4185841751 6.365046 -2.214102736 8.160565
## 2005.3315 2.796357 -0.5985764339 6.191290 -2.395745403 7.988459
## 2005.3342 3.458482 0.0604338113 6.856529 -1.738384052 8.655347
## 2005.3370 3.539810 0.1386498749 6.940970 -1.661815372 8.741435
## 2005.3397 4.363802 0.9595334996 7.768071 -0.842577626 9.570183
## 2005.3425 3.758230 0.3508545325 7.165605 -1.452900969 8.969361
## 2005.3452 3.127244 -0.2832348480 6.537723 -2.088633228 8.343121
## 2005.3479 2.907374 -0.5062052761 6.320953 -2.313245041 8.127993
## 2005.3507 3.905534 0.4888568206 7.322211 -1.319822840 9.130891
## 2005.3534 3.628857 0.2090851180 7.048630 -1.601232952 8.858948
## 2005.3562 3.599975 0.1771107999 7.022840 -1.634844199 8.834795
## 2005.3589 3.759797 0.3338432963 7.185751 -1.479747153 8.999342
## 2005.3616 3.254322 -0.1747185499 6.683363 -1.989942976 8.498587
## 2005.3644 3.533048 0.1009238453 6.965173 -1.715933089 8.782030
## 2005.3671 3.389051 -0.0461542045 6.824257 -1.864642181 8.642745
## 2005.3699 3.453453 0.0151687658 6.891737 -1.804948792 8.711854
## 2005.3726 2.461124 -0.9802357660 5.902483 -2.801981446 7.724229
## 2005.3753 3.253690 -0.1907424021 6.698122 -2.014114752 8.521495
## 2005.3781 3.161180 -0.2863228482 6.608682 -2.111320417 8.433680
## 2005.3808 2.947613 -0.5029568312 6.398183 -2.329578174 8.224804
## 2005.3836 3.285723 -0.1679113593 6.739358 -1.996155033 8.567601
## 2005.3863 3.622941 0.1662443339 7.079637 -1.663620232 8.909502
## 2005.3890 3.678382 0.2186259766 7.138137 -1.612858048 8.969621
## 2005.3918 3.070614 -0.3921986738 6.533426 -2.225300726 8.366528
## 2005.3945 3.293574 -0.1722917453 6.759440 -2.007010398 8.594159
## 2005.3973 3.300423 -0.1684941918 6.769340 -2.004828022 8.605674
## 2005.4000 3.755199 0.2832331848 7.227164 -1.554714404 9.065112
## 2005.4027 3.529622 0.0546105132 7.004633 -1.784949418 8.844193
## 2005.4055 2.987846 -0.4902085762 6.465901 -2.331379438 8.307071
## 2005.4082 2.847565 -0.6335304910 6.328660 -2.476310875 8.171440
## 2005.4110 2.973952 -0.5101812256 6.458084 -2.354569727 8.302473
## 2005.4137 3.396945 -0.0902229122 6.884113 -1.936218130 8.730108
## 2005.4164 3.526150 0.0359497291 7.016351 -1.811650808 8.863951
## 2005.4192 3.086001 -0.4072295355 6.579231 -2.256433999 8.428436
## 2005.4219 3.110623 -0.3856345922 6.606881 -2.236441592 8.457688
## 2005.4247 2.457786 -1.0414965905 5.957068 -2.893904739 7.809476
## 2005.4274 2.625129 -0.8771755268 6.127433 -2.731183443 7.981441
## 2005.4301 2.943813 -0.5615109796 6.449137 -2.417117283 8.304743
## 2005.4329 2.469123 -1.0392176178 5.977464 -2.896420933 7.834667
## 2005.4356 2.449614 -1.0617406992 5.960969 -2.920539654 7.819768
## 2005.4384 2.973090 -0.5412764092 6.487457 -2.401669636 8.347850
## 2005.4411 2.703488 -0.8138877237 6.220863 -2.675873856 8.082849
## 2005.4438 2.572985 -0.9473972327 6.093367 -2.810974910 7.956945
## 2005.4466 2.819954 -0.7034314773 6.343340 -2.568599341 8.208508
## 2005.4493 2.973583 -0.5528041278 6.499971 -2.419560824 8.366727
## 2005.4521 3.077371 -0.4520155765 6.606757 -2.320359754 8.475101
## 2005.4548 2.912194 -0.6201884704 6.444576 -2.490118781 8.314507
## 2005.4575 3.009123 -0.5262529150 6.544499 -2.397768014 8.416015
## 2005.4603 3.075898 -0.4624691864 6.614266 -2.335567734 8.487364
## 2005.4630 3.384883 -0.1564733700 6.926239 -2.031154028 8.800919
## 2005.4658 3.143759 -0.4005829031 6.688102 -2.276844338 8.564363
## 2005.4685 2.772826 -0.7745001063 6.320152 -2.652340987 8.197993
## 2005.4712 3.111874 -0.4384325966 6.662181 -2.317851596 8.541600
## 2005.4740 3.144519 -0.4087664938 6.697805 -2.289762287 8.578801
## 2005.4767 3.527727 -0.0285352675 7.083988 -1.911106535 8.966560
## 2005.4795 3.293097 -0.2661383132 6.852333 -2.150283737 8.736478
## 2005.4822 2.743152 -0.8190549475 6.305358 -2.704773214 8.191077
## 2005.4849 2.983511 -0.5816641246 6.548686 -2.468953922 8.435976
## 2005.4877 3.031971 -0.5361703074 6.600113 -2.425030329 8.488973
## 2005.4904 3.146489 -0.4246166322 6.717594 -2.315045574 8.608023
## 2005.4932 2.952027 -0.6220399623 6.526093 -2.514036523 8.418090
## 2005.4959 3.394896 -0.1821296691 6.971921 -2.075692551 8.865484
## 2005.4986 3.195302 -0.3846800225 6.775284 -2.279807930 8.670412
## 2005.5014 3.141474 -0.4414620443 6.724410 -2.338153687 8.621101
## 2005.5041 2.923191 -0.6626960589 6.509079 -2.560950149 8.407333
## 2005.5068 3.155422 -0.4334143015 6.744259 -2.333229553 8.644074
## 2005.5096 3.016617 -0.5751663486 6.608400 -2.476541481 8.509775
## 2005.5123 2.792930 -0.8017971895 6.387658 -2.704730923 8.290591
## 2005.5151 3.156801 -0.4408685170 6.754470 -2.345359576 8.658961
## 2005.5178 3.072207 -0.5284013452 6.672816 -2.434448458 8.578863
## 2005.5205 3.031100 -0.5724460812 6.634645 -2.480047978 8.542247
## 2005.5233 3.339231 -0.2672493270 6.945712 -2.176404742 8.854867
## 2005.5260 3.010581 -0.5988321307 6.619993 -2.509539801 8.530701
## 2005.5288 3.358299 -0.2540435060 6.970642 -2.166302171 8.882900
## 2005.5315 2.798293 -0.8169766632 6.413564 -2.730785066 8.327372
## 2005.5342 3.084867 -0.5333281148 6.703062 -2.448685002 8.618419
## 2005.5370 3.279240 -0.3418780749 6.900358 -2.258782195 8.817262
## 2005.5397 3.505831 -0.1182071222 7.129870 -2.036657228 9.048320
## 2005.5425 3.148788 -0.4781685894 6.775745 -2.398163435 8.695739
## 2005.5452 3.648061 0.0181885878 7.277933 -1.903349757 9.199472
## 2005.5479 3.047522 -0.5852640756 6.680307 -2.508344680 8.603388
## 2005.5507 3.415722 -0.2199745065 7.051419 -2.144596135 8.976041
## 2005.5534 3.036535 -0.6020701124 6.675141 -2.528231532 8.601302
## 2005.5562 2.952802 -0.6887100133 6.594314 -2.616409994 8.522014
## 2005.5589 3.228395 -0.4160208034 6.872811 -2.345258118 8.802049
## 2005.5616 3.511464 -0.1358533821 7.158782 -2.066626807 9.089556
## 2005.5644 3.180136 -0.4700816723 6.830353 -2.402389986 8.762661
## 2005.5671 2.898319 -0.7547950135 6.551434 -2.688636998 8.485276
## 2005.5699 3.356230 -0.2997790638 7.012240 -2.235153504 8.947614
## 2005.5726 3.154182 -0.5047203176 6.813084 -2.441626000 8.749989
## 2005.5753 3.758840 0.0970478529 7.420632 -1.841387863 9.359068
## 2005.5781 3.228186 -0.4364938522 6.892867 -2.376458395 8.832831
## 2005.5808 3.349316 -0.3182504867 7.016882 -2.259742652 8.958374
## 2005.5836 3.264179 -0.4062708220 6.934628 -2.349289409 8.877647
## 2005.5863 3.044852 -0.6284790776 6.718182 -2.573022888 8.662726
## 2005.5890 3.034840 -0.6413699188 6.711049 -2.587437757 8.657117
## 2005.5918 3.281519 -0.3975673121 6.960605 -2.345157986 8.908196
## 2005.5945 2.987035 -0.6949262048 6.668995 -2.644038525 8.618108
## 2005.5973 3.097615 -0.5872175940 6.782448 -2.537850372 8.733081
## 2005.6000 3.784652 0.0969486829 7.472355 -1.855203370 9.424507
## 2005.6027 4.038829 0.3482578444 7.729399 -1.605412302 9.683070
## 2005.6055 3.444853 -0.2485835089 7.138289 -2.203770569 9.093476
## 2005.6082 2.776498 -0.9198013983 6.472798 -2.876504197 8.429501
## 2005.6110 2.948794 -0.7503669090 6.647954 -2.708584273 8.606172
## 2005.6137 3.579169 -0.1228507133 7.281188 -2.082581471 9.240919
## 2005.6164 3.220736 -0.4841406163 6.925612 -2.445383601 8.886855
## 2005.6192 3.293723 -0.4140073081 7.001454 -2.376761355 8.964208
## 2005.6219 3.004188 -0.7063945951 6.714771 -2.670658541 8.679035
## 2005.6247 2.895269 -0.8181641856 6.608702 -2.783936871 8.574474
## 2005.6274 2.825361 -0.8909197103 6.541642 -2.858199978 8.508922
## 2005.6301 2.892591 -0.8265355943 6.611718 -2.795322290 8.580504
## 2005.6329 3.508446 -0.2135237846 7.230416 -2.183815756 9.200708
## 2005.6356 3.325353 -0.3994589211 7.050164 -2.371255020 9.021960
## 2005.6384 3.523310 -0.2043408492 7.250961 -2.177639929 9.224260
## 2005.6411 2.868934 -0.8615534147 6.599422 -2.836354331 8.574223
## 2005.6438 3.259458 -0.4738645980 6.992781 -2.450166209 8.969082
## 2005.6466 3.031638 -0.7045176115 6.767793 -2.682318780 8.745594
## 2005.6493 3.793565 0.0545788455 7.532551 -1.924720743 9.511850
## 2005.6521 3.725934 -0.0158801540 7.467749 -1.996677030 9.448545
## 2005.6548 3.205093 -0.5395472246 6.949734 -2.521840257 8.932027
## 2005.6575 2.863936 -0.8835288040 6.611401 -2.867316864 8.595189
## 2005.6603 3.304459 -0.4458278725 7.054746 -2.431109834 9.040028
## 2005.6630 3.155843 -0.5972642063 6.908949 -2.584038947 8.895724
## 2005.6658 2.840049 -0.9158754889 6.595974 -2.904141887 8.584240
## 2005.6685 2.707848 -1.0508923080 6.466588 -3.040649246 8.456345
## 2005.6712 2.795132 -0.9664223511 6.556685 -2.957668713 8.547932
## 2005.6740 3.059165 -0.7052000424 6.823531 -2.697934715 8.816265
## 2005.6767 3.324944 -0.4422304421 7.092119 -2.436452314 9.086341
## 2005.6795 3.290368 -0.4796144793 7.060350 -2.475322443 9.056058
## 2005.6822 3.332360 -0.4404276544 7.105147 -2.437620604 9.102340
## 2005.6849 3.567930 -0.2076603564 7.343520 -2.206337189 9.342197
## 2005.6877 3.691913 -0.0864783402 7.470305 -2.086637954 9.470464
## 2005.6904 3.241411 -0.5397798735 7.022601 -2.541421171 9.024242
## 2005.6932 3.113256 -0.6707312587 6.897243 -2.673853143 8.900365
## 2005.6959 3.496012 -0.2907706032 7.282794 -2.295371981 9.287395
## 2005.6986 3.445482 -0.3440929606 7.235057 -2.350172741 9.241137
## 2005.7014 3.180317 -0.6120481359 6.972683 -2.619605230 8.980240
## 2005.7041 2.915929 -0.8792256344 6.711083 -2.888258956 8.720116
## 2005.7068 2.697170 -1.1007709141 6.495111 -3.111279380 8.505619
## 2005.7096 3.285659 -0.5150668275 7.086384 -2.527049355 9.098367
## 2005.7123 2.625101 -1.1784070097 6.428609 -3.191862520 8.442064
## 2005.7151 2.654321 -1.1519675740 6.460609 -3.166894991 8.475537
## 2005.7178 3.179420 -0.6296470924 6.988487 -2.646045341 9.004885
## 2005.7205 3.334191 -0.4776528698 7.146034 -2.495520878 9.163902
## 2005.7233 3.125878 -0.6887395110 6.940496 -2.708076209 8.959833
## 2005.7260 3.821928 0.0045379240 7.639318 -2.016266396 9.660123
## 2005.7288 3.536404 -0.2837569501 7.356564 -2.306027827 9.378835
## 2005.7315 3.239520 -0.5834087285 7.062449 -2.607145100 9.086186
## 2005.7342 3.905553 0.0798572812 7.731248 -1.945343525 9.756449
## 2005.7370 3.479877 -0.3485829028 7.308337 -2.375247085 9.335001
## 2005.7397 3.201934 -0.6292884650 7.033156 -2.657414967 9.061282
## 2005.7425 3.228888 -0.6050941968 7.062871 -2.634681965 9.092459
## 2005.7452 3.152221 -0.6845197313 6.988962 -2.715567714 9.020010
## 2005.7479 3.900346 0.0608489698 7.739844 -1.971658179 9.772351
## 2005.7507 2.944691 -0.8975603632 6.786943 -2.931525632 8.820909
## 2005.7534 3.673922 -0.1710825232 7.518926 -2.206504866 9.554348
## 2005.7562 3.847909 0.0001536754 7.695663 -2.036724700 9.732542
## 2005.7589 3.778530 -0.0719734894 7.629033 -2.110306857 9.667367
## 2005.7616 3.115121 -0.7381292555 6.968371 -2.777916577 9.008158
## 2005.7644 3.357914 -0.4980810282 7.213908 -2.539321269 9.255148
## 2005.7671 3.465230 -0.3935076841 7.323967 -2.436199810 9.366659
## 2005.7699 3.754470 -0.1070075652 7.615948 -2.151150545 9.660091
## 2005.7726 3.840091 -0.0241254872 7.704308 -2.069718292 9.749901
## 2005.7753 3.983698 0.1167440623 7.850651 -1.930297541 9.897693
## 2005.7781 3.932843 0.0631547611 7.802532 -1.985334616 9.851021
## 2005.7808 3.782285 -0.0901369659 7.654706 -2.140073094 9.704642
## 2005.7836 3.325113 -0.5500395226 7.200266 -2.601421381 9.251647
## 2005.7863 3.301687 -0.5761947073 7.179569 -2.629021278 9.232395
## 2005.7890 3.602056 -0.2785529695 7.482665 -2.332823237 9.536935
## 2005.7918 3.280751 -0.6025833210 7.164085 -2.658296271 9.219798
## 2005.7945 3.376233 -0.5098246029 7.262291 -2.566979224 9.319445
## 2005.7973 3.557491 -0.3312881344 7.446270 -2.389883417 9.504865
## 2005.8000 4.054772 0.1632738099 7.946271 -1.896761126 10.006306
## 2005.8027 3.839486 -0.0547304856 7.733702 -2.116204070 9.795176
## 2005.8055 3.100940 -0.7959924505 6.997872 -2.858903680 9.060783
## 2005.8082 3.573701 -0.3259444787 7.473347 -2.390292352 9.537695
## 2005.8110 3.822717 -0.0796405466 7.725075 -2.145424064 9.790859
## 2005.8137 3.463569 -0.4414995475 7.368637 -2.508717713 9.435855
## 2005.8164 3.313529 -0.5942469903 7.221306 -2.662898809 9.289957
## 2005.8192 3.821311 -0.0891712412 7.731794 -2.159255719 9.801879
## 2005.8219 3.742743 -0.1704443990 7.655930 -2.241960546 9.727446
## 2005.8247 2.114504 -1.8013859517 6.030394 -3.874332779 8.103340
## 2005.8274 2.346998 -1.5715922381 6.265589 -3.645968759 8.339965
## 2005.8301 3.099915 -0.8213746528 7.021204 -2.897179883 9.097009
## 2005.8329 3.050182 -0.8738047746 6.974168 -2.951037731 9.051401
## 2005.8356 2.909701 -1.0169810178 6.836382 -3.095640719 8.915042
## 2005.8384 3.267784 -0.6615908605 7.197159 -2.741676329 9.277245
## 2005.8411 3.446398 -0.4856681162 7.378465 -2.567178375 9.459975
## 2005.8438 3.057415 -0.8773414066 6.992171 -2.960275481 9.075105
## 2005.8466 3.523398 -0.4140455495 7.460842 -2.498402467 9.545199
## 2005.8493 3.797508 -0.1426216568 7.737638 -2.228400447 9.823417
## 2005.8521 2.847015 -1.0957987704 6.789829 -3.182998465 8.877029
## 2005.8548 2.991343 -0.9541531348 6.936840 -3.042772766 9.025459
## 2005.8575 3.716269 -0.2319081126 7.664446 -2.321946717 9.754484
## 2005.8603 3.934839 -0.0160161813 7.885695 -2.107472795 9.977152
## 2005.8630 4.406596 0.4530634181 8.360128 -1.639810245 10.453002
## 2005.8658 3.526536 -0.4296713781 7.482744 -2.523961131 9.577033
## 2005.8685 3.837702 -0.1211783924 7.796583 -2.216883279 9.892288
## 2005.8712 3.596493 -0.3650591735 7.558045 -2.462178238 9.655164
## 2005.8740 3.857116 -0.1071061238 7.821338 -2.205638414 9.919870
## 2005.8767 3.906089 -0.0608009698 7.872978 -2.160745535 9.972923
## 2005.8795 3.270415 -0.6991406786 7.239971 -2.800496569 9.341327
## 2005.8822 3.333994 -0.6382261969 7.306214 -2.740992465 9.408980
## 2005.8849 4.122678 0.1477950401 8.097560 -1.956380661 10.201736
## 2005.8877 3.804409 -0.1731340201 7.781952 -2.278718210 9.887537
## 2005.8904 3.789673 -0.1905296361 7.769875 -2.297521374 9.876866
## 2005.8932 3.714606 -0.2682537611 7.697465 -2.376652107 9.805863
## 2005.8959 3.560560 -0.4249547340 7.546075 -2.534758750 9.655879
## 2005.8986 3.547938 -0.4402306503 7.536106 -2.551439400 9.647315
## 2005.9014 3.972143 -0.0186773146 7.962963 -2.131289865 10.075575
## 2005.9041 3.755462 -0.2380086099 7.748932 -2.352024028 9.862947
## 2005.9068 3.448248 -0.5478708836 7.444366 -2.663288240 9.559783
## 2005.9096 4.557044 0.5582788895 8.555809 -1.558539476 10.672627
## 2005.9123 5.271880 1.2704705741 9.273290 -0.847747874 11.391509
## 2005.9151 5.449443 1.4453896494 9.453496 -0.674227956 11.573113
## 2005.9178 3.386854 -0.6198406202 7.393548 -2.740856461 9.514564
## 2005.9205 4.479393 0.4700595500 8.488727 -1.652353604 10.611140
## 2005.9233 4.873154 0.8611823952 8.885126 -1.262627153 11.008935
## 2005.9260 4.640047 0.6254390932 8.654655 -1.499765932 10.779860
## 2005.9288 4.375590 0.3583474845 8.392832 -1.768252102 10.519432
## 2005.9315 5.339619 1.3197439159 9.359494 -0.808249318 11.487487
## 2005.9342 3.647156 -0.3753495426 7.669662 -2.504735511 9.799048
## 2005.9370 3.993534 -0.0316015186 8.018669 -2.162379312 10.149446
## 2005.9397 3.401641 -0.6261215839 7.429404 -2.758290294 9.561572
## 2005.9425 3.873255 -0.1571330523 7.903644 -2.290691771 10.037202
## 2005.9452 3.798746 -0.2342662713 7.831759 -2.369214095 9.966706
## 2005.9479 4.834415 0.7987800559 8.870050 -1.337555969 11.006386
## 2005.9507 4.485037 0.4467810860 8.523292 -1.690942239 10.661015
## 2005.9534 4.628231 0.5873570361 8.669106 -1.551752688 10.808216
## 2005.9562 3.974883 -0.0686086504 8.018375 -2.209103877 10.158870
## 2005.9589 3.930952 -0.1151552626 7.977059 -2.257035095 10.118939
## 2005.9616 4.343130 0.2944088533 8.391851 -1.848854690 10.535115
## 2005.9644 3.899447 -0.1518859711 7.950781 -2.296532333 10.095427
## 2005.9671 4.009766 -0.0441781026 8.063710 -2.190206392 10.209738
## 2005.9699 4.319703 0.2631504770 8.376256 -1.884258851 10.523665
## 2005.9726 3.333536 -0.7256236511 7.392696 -2.874413130 9.541486
## 2005.9753 4.017467 -0.0442988576 8.079232 -2.194467601 10.229401
## 2005.9781 4.172191 0.1078220493 8.236561 -2.043725074 10.388108
## 2005.9808 4.346757 0.2797858856 8.413729 -1.873138736 10.566653
## 2005.9836 4.706885 0.6373135743 8.776457 -1.516987665 10.930759
## 2005.9863 4.760269 0.6880985886 8.832440 -1.467578389 10.988117
## 2005.9890 4.496551 0.4217830165 8.571319 -1.735268821 10.728371
## 2005.9918 4.115070 0.0377064567 8.192433 -2.120719366 10.350859
## 2005.9945 3.541175 -0.5387826662 7.621132 -2.698581600 9.780931
## 2005.9973 3.419677 -0.6628724501 7.502227 -2.824043622 9.663398
## 2006.0000 3.636529 -0.4486110401 7.721669 -2.611153580 9.884212
## 2006.0027 4.057684 -0.0300447444 8.145413 -2.193957783 10.309326
## 2006.0055 4.086440 -0.0038765619 8.176756 -2.169159232 10.342039NOTE: #AIC = 16371.83 , BIC = 16388.91, RMSE = 0.8912478 Also, the headline of the plot below contains ETS(A,N,N) showing that the automated model characterized error of the “tsWSR_PK” SERIES as Additative (A), trend as None (A) and seasonality as None (N) which is equivalent to simple exponential model(ses) with only alpha parameter i.e level.
#Model 2 : ARIMA Models(AutoRegressive Moving Average)
It is used for forecasting for both seasonal and non- seasonal level.
#Changing to stationary set
train.sta <- diff(train)
test.sta <- diff(test)2.1 Auto Arima model without sesonality:
set.seed(301)
model <- auto.arima(train.sta, seasonal = FALSE)
summary(model)## Series: train.sta
## ARIMA(1,0,3) with zero mean
##
## Coefficients:
## ar1 ma1 ma2 ma3
## -0.8918 0.2659 -0.8286 -0.2770
## s.e. 0.0745 0.0753 0.0529 0.0247
##
## sigma^2 estimated as 0.9689: log likelihood=-3074.56
## AIC=6159.11 AICc=6159.14 BIC=6187.58
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -0.006952857 0.9834439 0.7398732 NaN Inf 0.5795203 0.005148871NOTE: #AIC = 6159.11 , BIC = 6187.58, RMSE = 0.9834439
tsdisplay(residuals(model), lag.max = 45, main = '(1,1,1) Model Residuals')
2.2. Auto Arima model with sesonality:
set.seed(301)
model2 <- auto.arima(train.sta, seasonal= TRUE)
summary(model2)## Series: train.sta
## ARIMA(1,0,3) with zero mean
##
## Coefficients:
## ar1 ma1 ma2 ma3
## -0.8918 0.2659 -0.8286 -0.2770
## s.e. 0.0745 0.0753 0.0529 0.0247
##
## sigma^2 estimated as 0.9689: log likelihood=-3074.56
## AIC=6159.11 AICc=6159.14 BIC=6187.58
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -0.006952857 0.9834439 0.7398732 NaN Inf 0.5795203 0.005148871NOTE: #AIC = 6159.11 , BIC = 6187.58, RMSE = 0.9834439
tsdisplay(residuals(model2), lag.max = 20, main = 'Seasonal Model Residuals')
NOTE: Above Graphs shows serious lags at 17, so modify model for p or q = 17
- Manual ARIMA:
Passing parameter order = (1,0,18) which means p(member of lags of a variable to be used as a predictor) = 1, d = 0(members of differences needed for stationarity) and q = 18 (moving average order - number of lagged forecasts error in the prediction equation)
set.seed(301)
model1 <- arima(train.sta, order = c(1,0,18))
summary(model1)##
## Call:
## arima(x = train.sta, order = c(1, 0, 18))
##
## Coefficients:
## ar1 ma1 ma2 ma3 ma4 ma5 ma6 ma7
## 0.0870 -0.7079 -0.1979 -0.0288 0.0159 -0.0087 0.0193 -0.0193
## s.e. 0.3104 0.3097 0.1940 0.0810 0.0309 0.0267 0.0265 0.0273
## ma8 ma9 ma10 ma11 ma12 ma13 ma14 ma15
## 0.0246 -0.0385 0.0548 -0.0159 -0.0182 -0.0287 0.0227 0.0300
## s.e. 0.0272 0.0269 0.0284 0.0307 0.0272 0.0267 0.0298 0.0272
## ma16 ma17 ma18 intercept
## -0.0258 -0.0647 0.0573 -0.0005
## s.e. 0.0285 0.0281 0.0235 0.0016
##
## sigma^2 estimated as 0.9595: log likelihood = -3065.9, aic = 6173.8
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -0.001369022 0.9795425 0.7387716 NaN Inf 0.5469141 -9.531875e-05NOTE: #AIC = 6173.8 , RMSE = 0.9795425
tsdisplay(residuals(model1), lag.max = 20, main = 'Seasonal Model Residuals')
Note: It seems good fit.
Fit the observed with the predicted values for both method models in the same plot.
par(mfrow = c(2,2))
fit_auto_train %>% forecast(h=341) %>% autoplot() + autolayer(test)
model1 %>% forecast(h=341) %>% autoplot() 
model2 %>% forecast(h=341) %>% autoplot() 
model %>% forecast(h=341) %>% autoplot()
COMMENT:
1. The plots includes 80% to 95% confidence interval.
2. For ARIMA models it plots the forecast but because of the nature of autoregressive process of 1 lag i.e. AR1, these forecast stabilizes quite smoothly.
Plot and comment on the residuals of the fitted data for both models in the same plot.
Residual Plot - to confirm no problem with this model
par(mfrow= c(2,2))
hist(fit_auto_train$residuals,col = 'red',xlab = 'Error',main = 'Histogram Of Residuals',freq= FALSE)
lines(density(model$residuals))
hist(model$residuals,col = 'red',xlab = 'Error',main = 'Histogram Of Residuals',freq= FALSE)
lines(density(model$residuals))
hist(model1$residuals,col = 'red',xlab = 'Error',main = 'Histogram Of Residuals',freq= FALSE)
lines(density(model$residuals))
hist(model2$residuals,col = 'red',xlab = 'Error',main = 'Histogram Of Residuals',freq= FALSE)
lines(density(model$residuals))
OBSERVATION: The residuals for each model are normally distributed, which shows the good fit of the models. It is normally distrbuted.
Testing the autocorrelation and partial autocorrelation of the residuals (using the plots and Ljung-Box Q statistic) up to an appropriate lag *
- ACF & PACF Plots
ACF(Autocorelation functions): These gives number of moving average(MA) terms in the model.
PACF(Partial Autocorelation Factors): There gives the number of AR terms in the model.
par(mfrow = c(2,2))
acf(fit_auto_train$residuals, main = 'Correlogram')
acf(model$residuals, main = 'Correlogram')
acf(model1$residuals, main = 'Correlogram')
acf(model2$residuals, main = 'Correlogram')
par(mfrow = c(2,2))
pacf(fit_auto_train$residuals, main = 'Partial Corelogram')
pacf(model$residuals, main = 'Partial Corelogram')
pacf(model1$residuals, main = 'Partial Corelogram')
pacf(model2$residuals, main = 'Partial Corelogram')
NOTE:
1. Residuals are the difference between actaual and fitted values
2. These blue lines are signficance bounds.
3. This graph shows us the autocorelations for insample forecast errors
4. Do not exceed these significance bounds for lags 1 to end
Here, our model produce residuals that are normal.It is not exhibiting any pattern or structure, this sums to have a consistant variance.
- Ljunx-Box Test to check the autocorelations of the residuals
This test used to test the lack of fit of a time series model. This test is applied to the residuals of the time series model
HO: No serial correlation upto 20 lags (does not exhibit lack of fit of the model) Ha: Serial corelation is present (the model exhibits lack of fit)
We reject the null hypothesis, if p value is less than 0.05. This test is generally done for ARIMA models
Box.test(model$residuals, lag =20, type = 'Ljung-Box')##
## Box-Ljung test
##
## data: model$residuals
## X-squared = 16.716, df = 20, p-value = 0.6713Box.test(model1$residuals, lag =20, type = 'Ljung-Box')##
## Box-Ljung test
##
## data: model1$residuals
## X-squared = 1.1949, df = 20, p-value = 1Box.test(model2$residuals, lag =20, type = 'Ljung-Box')##
## Box-Ljung test
##
## data: model2$residuals
## X-squared = 16.716, df = 20, p-value = 0.6713OBSERVATIONS:
For above performed Ljunx-Box Test on model,model1 and model2 output, we can say that p-value is more than significance level 0.05, then there is not a statistical significance. We conclude that there is a liitle evidence of non-zero auto-corelations in the insample forecast errors at lags 1 to 20.
So we fail to rejects the null hypothesis. Hence, we conclude that there is no serial auto corelation present between lags. Hence, the model seems to be good fit.
Test and comment on the normality of the residuals.
Here, further testing the normality by plotting Normal Q-Q plots. From below plots we observed that most of the datapoints lies on the line. Hence, we could conclude that our model produces residuals that are normal
par(mfrow = c(2,2))
qqnorm(fit_auto_train$residuals)
qqnorm(model$residuals)
qqnorm(model1$residuals)
qqnorm(model2$residuals)
Validating The Model by testing the model performance with Holdout set
Here, choosing RMSE as evaluation parameter. The lower RMSE indicates a more accurate forecast.
Below, is the comparison of model. We are fitting the model to test set which is the holdout set. And checking the accuracy using RMSE(Root mean square error) evaluation parameter.
accuracy(forecast(fit_auto_train), test) ["Test set", "RMSE"]## [1] 1.273901#o/p - 1.273901accuracy(forecast(model1), test.sta) ["Test set", "RMSE"]## [1] 1.253145#O/P - 1.253145accuracy(forecast(model2), test.sta) ["Test set", "RMSE"]## [1] 1.253728#o/p - 1.253728accuracy(forecast(model), test.sta) ["Test set", "RMSE"]## [1] 1.253728#O/P - 1.253728NOTE:- Here, the RMSE value is less of ARIMA models compared to exponential model.
The minimum RMSE is of model1.
The RMSE of auto arima models with seasonality and without seasonality have no difference. It gives the same result for this series.
COMMENT ON BEST MODEL AND ITS PARAMETERS We observed the best model to be ARIMA model i.e.“model1”.
summary(model1)##
## Call:
## arima(x = train.sta, order = c(1, 0, 18))
##
## Coefficients:
## ar1 ma1 ma2 ma3 ma4 ma5 ma6 ma7
## 0.0870 -0.7079 -0.1979 -0.0288 0.0159 -0.0087 0.0193 -0.0193
## s.e. 0.3104 0.3097 0.1940 0.0810 0.0309 0.0267 0.0265 0.0273
## ma8 ma9 ma10 ma11 ma12 ma13 ma14 ma15
## 0.0246 -0.0385 0.0548 -0.0159 -0.0182 -0.0287 0.0227 0.0300
## s.e. 0.0272 0.0269 0.0284 0.0307 0.0272 0.0267 0.0298 0.0272
## ma16 ma17 ma18 intercept
## -0.0258 -0.0647 0.0573 -0.0005
## s.e. 0.0285 0.0281 0.0235 0.0016
##
## sigma^2 estimated as 0.9595: log likelihood = -3065.9, aic = 6173.8
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -0.001369022 0.9795425 0.7387716 NaN Inf 0.5469141 -9.531875e-05model1$coef## ar1 ma1 ma2 ma3 ma4 ma5
## 0.087015549 -0.707885319 -0.197873344 -0.028846474 0.015867352 -0.008672255
## ma6 ma7 ma8 ma9 ma10 ma11
## 0.019276027 -0.019316858 0.024581787 -0.038470988 0.054800729 -0.015859729
## ma12 ma13 ma14 ma15 ma16 ma17
## -0.018230722 -0.028693866 0.022711597 0.030005760 -0.025773729 -0.064668514
## ma18 intercept
## 0.057287130 -0.000485985Passing parameter order = (1,0,18) ,which means
p = 1, d = 0 q = 18
For the best model, 1 member of lag is used as a predictor. As we transformed the series to stationary so members of differences needed for stationarity is 0. 18 are the number of lagged forecasts errors used in the prediction equation. AIC = 6173.8, RMSE = 0.9795425 which is minimum as compared to other models.
FOR VARIABLE 2
2. Forecasting on Peak T (T_PK)
#Checking the attributes of time series
attributes(tsT_PK)## $tsp
## [1] 1998.00 2004.94 365.00
##
## $class
## [1] "ts"#Plotting the series
plot(tsT_PK, main = "Peak tsT_PK", col = "red")
From the plot, we observes that there is no trend but seems to have seasonlity.
Most of the data is missing for year 2002 to 2003.
Checking the statistics and visualising the missing data in the series:
plotNA.distribution(tsT_PK)
As we see there is a large gap in the missing data, so locf and NOCB would not seems the good technique to implement here.
Hence, using “Linear interpolation” technique to impute missing values. This method works good for series having seasonality but no trend type of time series data.
#Impute the missing values with “na_interpolation” function of “imputeTS package” and visualise the imputed values in the time series
tsT_PK.imp <- na_interpolation(tsT_PK, method = "linear")
plotNA.imputations(tsT_PK, tsT_PK.imp)
#Decomposition Of Time Series
decomp1 <- decompose(tsT_PK.imp)
plot(decomp1, col = "red")
OBSERVATIONS:
1)There does not seems to have any trend.
2)We observe some seasonality in the series. Means there is some seasonality. Seasonality describes cyclical effects due to the time of the year.
Let’s explore this seasonality pattern by plotting the decomp$seasonal components such that y-axis represents Seasonality Index and x-axis.
#Visualising the seasonal component
par(mfrow=c(1,2))
plot(decomp1$seasonal, type ='b', xlab = 'Years', ylab = 'Seasonality Index', col = 'blue', las = 2, main = "SEASONAL DATA")
plot(decomp1$seasonal[1:400], type ='b', xlab = 'Years', ylab = 'Seasonality Index', col = 'blue', las = 2, main = "SEASONAL DATA")
OBSERVATION
1) There is increase in the mid of months of a year.
2) There is a drop in peak T for starting and ending months of the year
#Stationarity check of time series
We could check the stationarity of time series by ADF and KPSS Tests:
Augmented Dickey- Fuller(ADF) t-statistic test for unit root and Kwiatkowski-Phillips-Schmidt-Shin (KPSS) for level or trend stationarity Tests:
adf.test(tsT_PK.imp)##
## Augmented Dickey-Fuller Test
##
## data: tsT_PK.imp
## Dickey-Fuller = -3.8863, Lag order = 13, p-value = 0.01467
## alternative hypothesis: stationary##It results stationary, as p-value is less than 0.05
kpss.test(tsT_PK.imp, null="Trend")##
## KPSS Test for Trend Stationarity
##
## data: tsT_PK.imp
## KPSS Trend = 0.18987, Truncation lag parameter = 8, p-value = 0.0198NOTE: It results non- stationary as p-value is less than 0.05. More p-value means stationary series
par(mfrow=c(1,1))
acf(tsT_PK.imp,lag.max = length(tsT_PK.imp),xlab = "lag #", ylab = 'ACF',main='Statiionary Check ')
#Here, most of the lags are outside the significance bound, which means data is not stationary
#difference of 2 is sufficient
acf(diff(tsT_PK.imp, diff = 2))
Here, we observes most of the data lies outside the blue-dotted lines means the significance level. Now, we will take the difference to make our data stationary.
It seems difference of 2 is sufficient to make the series stationary
tsT_PK.sta <- diff(tsT_PK.imp, diff = 2)
attributes(tsT_PK.sta)## $tsp
## [1] 1998.005 2004.940 365.000
##
## $class
## [1] "ts"acf(tsT_PK.sta, lag.max = length(tsT_PK.sta),xlab = "lag #", ylab = 'ACF',main='Statiionary Check ')
Hence, after differencing our series is now transformed to stationary time series.
#Visualising the stationary series
plot(tsT_PK.sta, col = "red")
CREATING MODELS AND FORECASTING: USING EXPONENTIAL SMOOTHING AND ARIMA TECHNIQUES FOR TIME SERIES FORECASTING
1.Train - Test Split of the data
train1 <- window(tsT_PK.imp, end = c(2004, 3))
test1 <- window(tsT_PK.imp, start = c(2004, 4))#Model 1 : Auto Exponential Smoothening Model
set.seed(301)
fit_auto_train_VAR2 <- forecast(train1)
summary(fit_auto_train_VAR2)##
## Forecast method: STL + ETS(A,N,N)
##
## Model Information:
## ETS(A,N,N)
##
## Call:
## ets(y = na.interp(x), model = etsmodel, allow.multiplicative.trend = allow.multiplicative.trend)
##
## Smoothing parameters:
## alpha = 0.8786
##
## Initial states:
## l = 25.3318
##
## sigma: 2.9034
##
## AIC AICc BIC
## 21549.73 21549.74 21566.81
##
## Error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set 0.002767155 2.902054 2.029788 -2.028444 11.01258 0.4517796
## ACF1
## Training set 0.02845628
##
## Forecasts:
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 2004.0082 21.33776 17.61692695 25.05859 15.64723876 27.02827
## 2004.0110 22.07243 17.11954862 27.02532 14.49764993 29.64722
## 2004.0137 20.91589 14.98145198 26.85033 11.83995012 29.99183
## 2004.0164 24.55218 17.77692819 31.32743 14.19032603 34.91404
## 2004.0192 21.65143 14.12876170 29.17410 10.14650151 33.15636
## 2004.0219 19.43034 11.22808227 27.63260 6.88606921 31.97461
## 2004.0247 24.41696 15.58726690 33.24666 10.91310830 37.92082
## 2004.0274 25.88847 16.47305495 35.30388 11.48883588 40.28810
## 2004.0301 26.02004 16.05326952 35.98681 10.77717997 41.26290
## 2004.0329 24.37379 13.88460805 34.86298 8.33196885 40.41562
## 2004.0356 22.24627 11.25948520 33.23306 5.44343128 39.04911
## 2004.0384 23.14929 11.68647891 34.61210 5.61843438 40.68014
## 2004.0411 22.54337 10.62352985 34.46320 4.31355001 40.77318
## 2004.0438 21.98502 9.62504852 34.34500 3.08207315 40.88797
## 2004.0466 22.87562 10.09065104 35.66059 3.32269655 42.42855
## 2004.0493 21.75903 8.56274360 34.95532 1.57705185 41.94101
## 2004.0521 20.15676 6.56160118 33.75193 -0.63524329 40.94877
## 2004.0548 23.04116 9.05849259 37.02382 1.65651640 44.42580
## 2004.0575 24.01153 9.65181564 38.37125 2.05024128 45.97282
## 2004.0603 22.03129 7.30417561 36.75841 -0.49188838 44.55447
## 2004.0630 23.25205 8.16647812 38.33762 0.18065976 46.32344
## 2004.0658 22.64902 7.21331587 38.08472 -0.95785150 46.25589
## 2004.0685 21.70167 5.92360718 37.47974 -2.42879711 45.83215
## 2004.0712 24.45815 8.34499435 40.57131 -0.18479688 49.10110
## 2004.0740 27.08434 10.64291370 43.52576 1.93935008 52.22932
## 2004.0767 24.61971 7.85644823 41.38297 -1.01748555 50.25690
## 2004.0795 22.56057 5.48153632 39.63960 -3.55955775 48.68070
## 2004.0822 26.20633 8.81725384 43.59540 -0.38796550 52.80062
## 2004.0849 27.16862 9.47493726 44.86230 0.10846811 54.22877
## 2004.0877 27.43497 9.44183281 45.42810 -0.08315672 54.95309
## 2004.0904 26.50902 8.22133846 44.79670 -1.45957610 54.47762
## 2004.0932 24.08115 5.50358572 42.65871 -4.33078197 52.49308
## 2004.0959 21.82315 2.96015892 40.68614 -7.02530396 50.67160
## 2004.0986 22.29209 3.14793227 41.43625 -6.98637334 51.57056
## 2004.1014 22.35538 2.93412259 41.77664 -7.34687111 52.05764
## 2004.1041 25.56391 5.86944691 45.25837 -4.55617118 55.68399
## 2004.1068 26.88179 6.91786653 46.84572 -3.65039699 57.41398
## 2004.1096 24.08666 3.85686493 44.31646 -6.85214412 55.02547
## 2004.1123 24.97278 4.48055506 45.46501 -6.36737359 56.31293
## 2004.1151 27.03969 6.28836116 47.79103 -4.69673043 58.77612
## 2004.1178 26.98740 5.98015473 47.99464 -5.14040813 59.11520
## 2004.1205 24.71339 3.45331218 45.97346 -7.80109138 57.22786
## 2004.1233 24.44516 2.93523097 45.95510 -8.45144022 57.34177
## 2004.1260 24.73349 2.97656894 46.49042 -8.54085100 58.00784
## 2004.1288 23.06029 1.05914938 45.06143 -10.58755157 56.70813
## 2004.1315 24.47462 2.23194310 46.71730 -9.54261950 58.49186
## 2004.1342 22.49757 0.01594875 44.97919 -11.88510186 56.88024
## 2004.1370 24.51444 1.79639514 47.23249 -10.22981319 59.25870
## 2004.1397 25.71179 2.75974791 48.66383 -9.39032895 60.81391
## 2004.1425 27.11878 3.93510745 50.30245 -8.33758781 62.57515
## 2004.1452 28.42195 5.00893193 51.83496 -7.38516869 64.22906
## 2004.1479 29.21361 5.57347627 52.85373 -6.94085197 65.36806
## 2004.1507 28.66119 4.79610575 52.52627 -7.83730601 65.15968
## 2004.1534 26.46251 2.37457086 50.55044 -10.37681234 63.30183
## 2004.1562 25.81203 1.50328440 50.12078 -11.36498879 62.98905
## 2004.1589 26.59567 2.06809795 51.12324 -10.91601295 64.10735
## 2004.1616 27.09325 2.34879293 51.83771 -10.75013134 64.93663
## 2004.1644 25.46691 0.50745014 50.42637 -12.70528986 63.63911
## 2004.1671 28.32860 3.15597258 53.50123 -10.16961107 66.82681
## 2004.1699 28.63396 3.24995559 54.01796 -10.18752411 67.45544
## 2004.1726 27.89432 2.30068452 53.48795 -11.24776712 67.03640
## 2004.1753 28.70350 2.90193964 54.50506 -10.75658235 68.16359
## 2004.1781 26.77808 0.77025384 52.78591 -12.99745854 66.55362
## 2004.1808 23.92485 -2.28762375 50.13732 -16.16366733 64.01336
## 2004.1836 24.61371 -1.80182026 51.02923 -15.78535581 65.01277
## 2004.1863 25.29568 -1.32135257 51.91272 -15.41156008 66.00293
## 2004.1890 26.98864 0.17160973 53.80567 -14.02446821 68.00175
## 2004.1918 28.28190 1.26635503 55.29744 -13.03480961 69.59861
## 2004.1945 27.40945 0.19683862 54.62206 -14.20864614 69.02754
## 2004.1973 27.22046 -0.18779390 54.62872 -14.69684874 69.13777
## 2004.2000 27.09137 -0.51114390 54.69389 -15.12303473 69.30578
## 2004.2027 28.24861 0.45318248 56.04403 -14.26082563 70.75804
## 2004.2055 29.24106 1.25405833 57.22805 -13.56136323 72.04347
## 2004.2082 28.81009 0.63281800 56.98736 -14.28332752 71.90350
## 2004.2110 27.27129 -1.09497848 55.63755 -16.11117234 70.65375
## 2004.2137 27.38372 -1.17028859 55.93773 -16.28586861 71.05331
## 2004.2164 28.66551 -0.07502305 57.40603 -15.28934001 72.62035
## 2004.2192 28.20447 -0.72137501 57.13031 -16.03379225 72.44273
## 2004.2219 28.48983 -0.62015109 57.59981 -16.03004411 73.00970
## 2004.2247 29.36313 0.07017237 58.65609 -15.43658371 74.16285
## 2004.2274 28.66027 -0.81453250 58.13507 -16.41755033 73.73809
## 2004.2301 30.32187 0.66633877 59.97740 -15.03235055 75.67609
## 2004.2329 29.89718 0.06201610 59.73234 -15.73176520 75.52612
## 2004.2356 30.65006 0.63634031 60.66378 -15.25196384 76.55209
## 2004.2384 31.04096 0.84973810 61.23218 -15.13252988 77.21445
## 2004.2411 30.30644 -0.06125188 60.67412 -16.13693448 76.74981
## 2004.2438 30.78623 0.24310090 61.32937 -15.92545662 77.49792
## 2004.2466 30.04913 -0.66844845 60.76670 -16.92935043 77.02760
## 2004.2493 31.30543 0.41439567 62.19646 -15.93832932 78.54919
## 2004.2521 33.08384 2.02032051 64.14736 -14.42371475 80.59140
## 2004.2548 32.61044 1.37538078 63.84550 -15.15946053 80.38034
## 2004.2575 31.71915 0.31349493 63.12481 -16.31165645 79.74996
## 2004.2603 31.39872 -0.17661327 62.97406 -16.89158678 79.68903
## 2004.2630 32.58777 0.84366254 64.33188 -15.96065299 81.13619
## 2004.2658 32.74668 0.83468894 64.65866 -16.05849612 81.55185
## 2004.2685 33.30654 1.22755292 65.38553 -15.75403660 82.36711
## 2004.2712 31.93427 -0.31085389 64.17939 -17.38039003 81.24892
## 2004.2740 32.34723 -0.06317494 64.75763 -17.22020689 81.91467
## 2004.2767 31.07633 -1.49851740 63.65118 -18.74260121 80.89527
## 2004.2795 31.70973 -1.02873578 64.44820 -18.35943420 81.77890
## 2004.2822 33.52745 0.62617567 66.42872 -16.79070662 83.84561
## 2004.2849 33.81631 0.75302938 66.87958 -16.74961241 84.38223
## 2004.2877 34.71854 1.49404422 67.94303 -16.09393892 85.53101
## 2004.2904 33.56265 0.17772159 66.94757 -17.49519079 84.62049
## 2004.2932 32.95516 -0.58942907 66.49976 -18.34686451 84.25719
## 2004.2959 34.08581 0.38230611 67.78932 -17.45925196 85.63088
## 2004.2986 33.28464 -0.57702948 67.14631 -18.50231542 85.07160
## 2004.3014 32.72647 -1.29263462 66.74557 -19.30125914 84.75419
## 2004.3041 34.08326 -0.09254596 68.25907 -18.18412516 86.35065
## 2004.3068 34.56281 0.23101461 68.89461 -17.94314064 87.06876
## 2004.3096 35.08883 0.60174586 69.57591 -17.65461195 87.83227
## 2004.3123 34.57873 -0.06293523 69.22040 -18.40112711 87.55859
## 2004.3151 33.94761 -0.84795754 68.74318 -19.26761994 87.16285
## 2004.3178 34.60379 -0.34500234 69.55259 -18.84577649 88.05336
## 2004.3205 34.34280 -0.75854870 69.44415 -19.34008053 88.02568
## 2004.3233 34.68704 -0.56620742 69.94028 -19.22814747 88.60222
## 2004.3260 35.33943 -0.06505629 70.74392 -18.80705958 89.48592
## 2004.3288 33.25109 -2.30399878 68.80617 -21.12572475 87.62790
## 2004.3315 33.65895 -2.04610098 69.36400 -20.94721337 88.26511
## 2004.3342 34.75022 -1.10416680 70.60461 -20.08433358 89.58478
## 2004.3370 35.56147 -0.44163825 71.56457 -19.50053150 90.62347
## 2004.3397 33.69237 -2.45884581 69.84358 -21.59614168 88.98087
## 2004.3425 33.32458 -2.97413275 69.62330 -22.18951135 88.83867
## 2004.3452 33.92187 -2.52374875 70.36749 -21.81689405 89.66063
## 2004.3479 34.42248 -2.16945577 71.01441 -21.54005558 90.38501
## 2004.3507 36.00486 -0.73281106 72.74252 -20.18055689 92.19027
## 2004.3534 35.44893 -1.43388965 72.33176 -20.95847669 91.85634
## 2004.3562 36.04645 -0.98095997 73.07386 -20.58208699 92.67499
## 2004.3589 36.30524 -0.86619174 73.47668 -20.54356101 93.15405
## 2004.3616 35.72844 -1.58646020 73.04335 -21.33977746 92.79667
## 2004.3644 35.00293 -2.45489653 72.46075 -22.28387088 92.28973
## 2004.3671 35.79269 -1.80751286 73.39289 -21.71185673 93.29723
## 2004.3699 35.98889 -1.75314559 73.73093 -21.73257467 93.71036
## 2004.3726 35.91186 -1.97148441 73.79521 -22.02571757 93.84945
## 2004.3753 37.14052 -0.88360921 75.16465 -21.01236845 95.29341
## 2004.3781 35.88988 -2.27451795 74.05427 -22.47752837 94.25728
## 2004.3808 36.51058 -1.79356778 74.81472 -22.07055747 95.09171
## 2004.3836 37.04571 -1.39768214 75.48909 -21.74838218 95.83979
## 2004.3863 37.03063 -1.55149432 75.61276 -21.97563869 96.03690
## 2004.3890 36.23782 -2.48255205 74.95819 -22.97987760 95.45551
## 2004.3918 34.78053 -4.07759340 73.63865 -24.64783977 94.20889
## 2004.3945 35.16981 -3.82557248 74.16520 -24.46848208 94.80811
## 2004.3973 35.17821 -3.95395367 74.31038 -24.66927162 95.02570
## 2004.4000 36.17215 -3.09632803 75.44062 -23.88380212 96.22809
## 2004.4027 35.34017 -4.06414007 74.74448 -24.92352070 95.60386
## 2004.4055 37.02464 -2.51503685 76.56432 -23.44607699 97.49536
## 2004.4082 37.58937 -2.08520812 77.26396 -23.08766327 98.26641
## 2004.4110 37.88535 -1.92367769 77.69438 -22.99730585 98.76801
## 2004.4137 37.89229 -2.05073594 77.83532 -23.19529753 98.97988
## 2004.4164 38.08892 -1.98765823 78.16549 -23.20291609 99.38075
## 2004.4192 36.79556 -3.41412477 77.00524 -24.69984409 98.29096
## 2004.4219 37.00514 -3.33721067 77.34748 -24.69315898 98.70343
## 2004.4247 35.84085 -4.63372993 76.31543 -26.05967704 97.74137
## 2004.4274 35.85676 -4.74961724 76.46314 -26.24533520 97.95886
## 2004.4301 36.22227 -4.51547689 76.96003 -26.08073998 98.52529
## 2004.4329 36.00510 -4.86360488 76.87380 -26.49818953 98.50839
## 2004.4356 37.19863 -3.80060394 78.19787 -25.50428875 99.90155
## 2004.4384 36.94062 -4.18873697 78.06997 -25.96130263 99.84254
## 2004.4411 37.36744 -3.89162804 78.62650 -25.73285733 100.46773
## 2004.4438 36.09036 -5.29800451 77.47873 -27.20768223 99.38841
## 2004.4466 35.88632 -5.63094128 77.40359 -27.60885426 99.38150
## 2004.4493 36.72876 -4.91701125 78.37452 -26.96294829 100.42046
## 2004.4521 37.34582 -4.42805647 79.11969 -26.54180833 101.23344
## 2004.4548 36.14395 -5.75763480 78.04554 -27.93899414 100.22690
## 2004.4575 35.84355 -6.18536232 77.87246 -28.43412372 100.12122
## 2004.4603 36.94056 -5.21528971 79.09641 -27.53124958 101.41237
## 2004.4630 36.07806 -6.20435075 78.36047 -28.58730735 100.74343
## 2004.4658 36.46989 -5.93870248 78.87848 -28.38845586 101.32824
## 2004.4685 37.07900 -5.45539966 79.61340 -27.97175168 102.12976
## 2004.4712 37.10515 -5.55469317 79.76498 -28.13744742 102.34774
## 2004.4740 37.39795 -5.38695621 80.18286 -28.03591801 102.83182
## 2004.4767 36.95492 -5.95468683 79.86454 -28.66966320 102.57951
## 2004.4795 37.27445 -5.75950157 80.30841 -28.54030123 103.08921
## 2004.4822 38.26726 -4.89068068 81.42520 -27.73711397 104.27163
## 2004.4849 37.79162 -5.48994894 81.07319 -28.40182785 103.98507
## 2004.4877 37.15979 -6.24505482 80.56464 -29.22219295 103.54178
## 2004.4904 37.91082 -5.61695992 81.43859 -28.65917244 104.48080
## 2004.4932 38.99040 -4.65996190 82.64075 -27.76706555 105.74786
## 2004.4959 39.05072 -4.72187804 82.82332 -27.89369109 105.99513
## 2004.4986 37.39602 -6.49847172 81.29052 -29.73481398 104.52686
## 2004.5014 37.62844 -6.38761682 81.64450 -29.68830956 104.94519
## 2004.5041 38.27069 -5.86658796 82.40798 -29.23145397 105.77284
## 2004.5068 37.46640 -6.79177409 81.72458 -30.22063759 105.15344
## 2004.5096 37.65882 -6.71991722 82.03757 -30.21260387 105.53025
## 2004.5123 38.54743 -5.95154646 83.04641 -29.50788334 106.60275
## 2004.5151 38.58190 -6.03699540 83.20079 -29.65681098 106.82061
## 2004.5178 38.66628 -6.07220177 83.40477 -29.75532592 107.08790
## 2004.5205 38.10379 -6.75397437 82.96155 -30.50023829 106.70781
## 2004.5233 38.99478 -5.98193298 83.97150 -29.79116925 107.78074
## 2004.5260 38.48007 -6.61529662 83.57543 -30.48733911 107.44747
## 2004.5288 37.93729 -7.27640664 83.15098 -31.21109055 107.08567
## 2004.5315 37.79885 -7.53286652 83.13057 -31.53002834 107.12773
## 2004.5342 37.30115 -8.14828932 82.75058 -32.20776679 106.81006
## 2004.5370 38.17304 -7.39380719 83.73989 -31.51543935 107.86152
## 2004.5397 38.72999 -6.95396483 84.41395 -31.13759191 108.59758
## 2004.5425 38.74992 -7.05085190 84.55069 -31.29631539 108.79615
## 2004.5452 37.73859 -8.17869735 83.65587 -32.48583994 107.96302
## 2004.5479 38.25482 -7.77868908 84.28832 -32.14735466 108.65699
## 2004.5507 37.44424 -8.70519666 83.59367 -33.13523030 108.02370
## 2004.5534 37.38363 -8.88143373 83.64870 -33.37268165 108.13995
## 2004.5562 37.20438 -9.17604005 83.58479 -33.72834964 108.13710
## 2004.5589 38.37489 -8.12058896 84.87037 -32.73380872 109.48359
## 2004.5616 38.50570 -8.10455491 85.11596 -32.77853448 109.78994
## 2004.5644 37.57373 -9.15102020 84.29849 -33.88561034 109.03308
## 2004.5671 38.29604 -8.54292649 85.13501 -33.33797903 109.93006
## 2004.5699 38.59821 -8.35469995 85.55112 -33.21006781 110.40648
## 2004.5726 38.57277 -8.49380083 85.63934 -33.40933801 110.55488
## 2004.5753 38.95516 -8.22480052 86.13512 -33.20036206 111.11068
## 2004.5781 38.77285 -8.52022591 86.06593 -33.55566789 111.10137
## 2004.5808 37.47278 -9.93313882 84.87871 -35.02831836 109.97389
## 2004.5836 37.80941 -9.70909091 85.32791 -34.86386615 110.48269
## 2004.5863 38.07499 -9.55582133 85.70581 -34.77005142 110.92004
## 2004.5890 38.72859 -9.01427092 86.47146 -34.28781598 111.74500
## 2004.5918 38.32938 -9.52526736 86.18403 -34.85798851 111.51675
## 2004.5945 38.52241 -9.44376743 86.48858 -34.83552677 111.88034
## 2004.5973 38.24781 -9.82963628 86.32525 -35.28029685 111.77591
## 2004.6000 38.93087 -9.25758224 87.11932 -34.76700804 112.62875
## 2004.6027 37.08008 -11.21912316 85.37929 -36.78717913 110.94735
## 2004.6055 35.98888 -12.42082428 84.39859 -38.04737627 110.02515
## 2004.6082 35.53528 -12.98467677 84.05524 -38.66959156 109.74016
## 2004.6110 35.90615 -12.72380444 84.53611 -38.46694972 110.27926
## 2004.6137 37.25580 -11.48390901 85.99551 -37.28515337 111.79676
## 2004.6164 37.52158 -11.32763107 86.37080 -37.18684397 112.23001
## 2004.6192 36.92394 -12.03453486 85.88242 -37.95158664 111.79947
## 2004.6219 35.27526 -13.79223172 84.34275 -39.76699359 110.31752
## 2004.6247 34.93507 -14.24120243 84.11133 -40.27354645 110.14368
## 2004.6274 36.29109 -12.99371777 85.57589 -39.08351685 111.66569
## 2004.6301 36.40665 -12.98645364 85.79975 -39.13358154 111.94687
## 2004.6329 36.14076 -13.36040468 85.64192 -39.56473598 111.84625
## 2004.6356 36.89777 -12.71121810 86.50675 -38.97262819 112.76816
## 2004.6384 36.57974 -13.13683574 86.29631 -39.45520083 112.61468
## 2004.6411 37.63636 -12.18757256 87.46029 -38.56276966 113.83549
## 2004.6438 37.81953 -12.11153153 87.75059 -38.54343845 114.18250
## 2004.6466 36.71302 -13.32493640 86.75098 -39.81343172 113.23948
## 2004.6493 36.32287 -13.82175878 86.46750 -40.36672188 113.01246
## 2004.6521 36.04087 -14.21020205 86.29194 -40.81151305 112.89325
## 2004.6548 34.90720 -15.45009209 85.26449 -42.10763188 111.92203
## 2004.6575 35.29591 -15.16737464 85.75920 -41.88102488 112.47285
## 2004.6603 34.90530 -15.66376377 85.47436 -42.43340684 112.24400
## 2004.6630 34.53673 -16.13787819 85.21135 -42.96339723 112.03686
## 2004.6658 34.72782 -16.05212940 85.50776 -42.93340826 112.38904
## 2004.6685 35.39459 -15.49047161 86.27965 -42.42739486 113.21657
## 2004.6712 35.64422 -15.34573310 86.63418 -42.33818602 113.62663
## 2004.6740 35.40171 -15.69293001 86.49635 -42.74079862 113.54422
## 2004.6767 34.11592 -17.08319198 85.31503 -44.18636296 112.41820
## 2004.6795 35.10043 -16.20293324 86.40380 -43.36129399 113.56216
## 2004.6822 35.30470 -16.10271174 86.71211 -43.31615033 113.92555
## 2004.6849 35.36310 -16.14814788 86.87434 -43.41655305 114.14274
## 2004.6877 33.27493 -18.33993446 84.88980 -45.66319565 112.21306
## 2004.6904 33.36470 -18.35359044 85.08298 -45.73159773 112.46099
## 2004.6932 32.42228 -19.39921355 84.24378 -46.83185769 111.67643
## 2004.6959 32.80239 -19.12211780 84.72689 -46.60929018 112.21406
## 2004.6986 31.29048 -20.73682986 83.31778 -48.27842253 110.85938
## 2004.7014 32.10386 -20.02604528 84.23377 -47.62195091 111.82967
## 2004.7041 32.82214 -19.41015996 85.05445 -47.06027188 112.70456
## 2004.7068 32.79602 -19.53848217 85.13052 -47.24269431 112.83473
## 2004.7096 32.64115 -19.79534975 85.07765 -47.55355667 112.83586
## 2004.7123 31.83624 -20.70205787 84.37455 -48.51415474 112.18664
## 2004.7151 32.26565 -20.37425987 84.90555 -48.24014248 112.77143
## 2004.7178 33.52658 -19.21473105 86.26790 -47.13429578 114.18746
## 2004.7205 33.56537 -19.27715676 86.40790 -47.25030060 114.38104
## 2004.7233 33.47551 -19.46803223 86.41906 -47.49465275 114.44568
## 2004.7260 33.41300 -19.63137054 86.45738 -47.71136589 114.53737
## 2004.7288 30.62072 -22.52429376 83.76573 -50.65756267 111.89900
## 2004.7315 30.19323 -23.05222157 83.43869 -51.23866336 111.62513
## 2004.7342 30.18195 -23.16376725 83.52766 -51.40328180 111.76717
## 2004.7370 29.55750 -23.88828212 83.00328 -52.18076987 111.29577
## 2004.7397 31.34930 -22.19636514 84.89496 -50.54172709 113.24032
## 2004.7425 32.07855 -21.56680894 85.72391 -49.96494665 114.12205
## 2004.7452 33.08041 -20.66445547 86.82528 -49.11527104 115.27610
## 2004.7479 32.90438 -20.93982056 86.74857 -49.44321664 115.25197
## 2004.7507 32.97420 -20.96914269 86.91754 -49.52502246 115.47342
## 2004.7534 32.59299 -21.44931250 86.63529 -50.05757967 115.24356
## 2004.7562 30.89193 -23.24915597 85.03301 -51.90971478 113.69357
## 2004.7589 29.06668 -25.17300581 83.30637 -53.88576103 112.01912
## 2004.7616 27.82460 -26.51350321 82.16271 -55.27836014 110.92757
## 2004.7644 29.49235 -24.94400385 83.92870 -53.76086827 112.74557
## 2004.7671 30.61111 -23.92331082 85.14553 -52.79208904 114.01431
## 2004.7699 31.43556 -23.19674980 86.06787 -52.11734864 114.98847
## 2004.7726 32.41830 -22.31173114 87.14832 -51.28405791 116.12065
## 2004.7753 32.49348 -22.33408555 87.32106 -51.35804806 116.34502
## 2004.7781 32.00232 -22.92261804 86.92726 -51.99812459 116.00277
## 2004.7808 30.64694 -24.37519545 85.66908 -53.50215481 114.79604
## 2004.7836 30.68177 -24.43739487 85.80093 -53.61571633 114.97925
## 2004.7863 30.74598 -24.47003372 85.96200 -53.69962702 115.19159
## 2004.7890 28.20937 -27.10332850 83.52207 -56.38410386 112.80285
## 2004.7918 27.97080 -27.43841926 83.38002 -56.77028736 112.71188
## 2004.7945 28.74415 -26.76141587 84.24972 -56.14428788 113.63259
## 2004.7973 28.98285 -26.61890078 84.58460 -56.05268832 114.01838
## 2004.8000 30.53876 -25.15900756 86.23652 -54.64362270 115.72114
## 2004.8027 31.08754 -24.70607308 86.88116 -54.24142835 116.41651
## 2004.8055 30.40679 -25.48251359 86.29609 -55.06852198 115.88210
## 2004.8082 29.89525 -26.08956952 85.88008 -55.72614445 115.51665
## 2004.8110 29.66012 -26.42005876 85.74031 -56.10711410 115.42736
## 2004.8137 30.53320 -25.64217808 86.70858 -55.37962814 116.44603
## 2004.8164 29.17009 -27.10032435 85.44051 -56.88808387 115.22827
## 2004.8192 28.24376 -28.12152954 84.60906 -57.95951369 114.44704
## 2004.8219 27.29625 -29.16376314 83.75626 -59.05188753 113.64438
## 2004.8247 28.10239 -28.45218213 84.65696 -58.39036278 114.59514
## 2004.8274 28.14285 -28.50611890 84.79182 -58.49427226 114.77997
## 2004.8301 29.10980 -27.63341043 85.85302 -57.67145336 115.89106
## 2004.8329 26.81817 -30.01913058 83.65547 -60.10698036 113.74332
## 2004.8356 25.08926 -31.84197277 82.02049 -61.97954708 112.15807
## 2004.8384 27.16000 -29.86501319 84.18501 -60.05223012 114.37222
## 2004.8411 28.63714 -28.48149143 85.75578 -58.71826949 115.99255
## 2004.8438 27.33552 -29.87658442 84.54762 -60.16284250 114.83388
## 2004.8466 24.49701 -32.80840742 81.80243 -63.14406482 112.13809
## 2004.8493 25.26265 -32.13593319 82.66124 -62.52090959 113.04622
## 2004.8521 25.11165 -32.37994664 82.60326 -62.81416213 113.03747
## 2004.8548 25.35216 -32.23230636 82.93663 -62.71568139 113.42000
## 2004.8575 26.19308 -31.48409793 83.87026 -62.01655336 114.40272
## 2004.8603 29.20590 -28.56384610 86.97565 -59.14530316 117.55711
## 2004.8630 26.40150 -31.46066302 84.26367 -62.09104332 114.89405
## 2004.8658 24.21487 -33.73956376 82.16931 -64.41878928 112.84853
## 2004.8685 25.53978 -32.50677995 83.58634 -63.23477304 114.31433
## 2004.8712 26.85189 -31.28664751 84.99043 -62.06333091 115.76711
## 2004.8740 24.90127 -33.32910458 83.13164 -64.15440136 113.95694
## 2004.8767 23.90887 -34.41319213 82.23093 -65.28702576 113.10476
## 2004.8795 23.80878 -34.60482829 82.22238 -65.52712258 113.14467
## 2004.8822 25.05204 -33.45297009 83.55704 -64.42364922 114.52772
## 2004.8849 23.43831 -35.15795102 82.03458 -66.17693950 113.05357
## 2004.8877 23.76433 -34.92305105 82.45171 -65.99027377 113.51893
## 2004.8904 25.34406 -33.43430026 84.12241 -64.54968245 115.23779
## 2004.8932 26.28641 -32.58278135 85.15560 -63.74624859 116.31907
## 2004.8959 24.99060 -33.96928433 83.95049 -65.18076253 115.16197
## 2004.8986 25.35943 -33.69100677 84.40988 -64.95042218 115.66929
## 2004.9014 26.16791 -32.97294757 85.30877 -64.28022681 116.61605
## 2004.9041 24.76349 -34.46764579 83.99463 -65.82271579 115.34970
## 2004.9068 25.16508 -34.15619496 84.48636 -65.55898299 115.88915
## 2004.9096 27.95376 -31.45752167 87.36505 -62.90795532 118.81548
## 2004.9123 25.43331 -34.06784597 84.93446 -65.56585318 116.43247
## 2004.9151 23.22653 -36.36435111 82.81742 -67.90986013 114.36293
## 2004.9178 23.51102 -36.16946267 83.19150 -67.76240208 114.78444
## 2004.9205 22.96464 -36.80530213 82.73459 -68.44560083 114.37489
## 2004.9233 24.85602 -35.00325271 84.71530 -66.69083992 116.40289
## 2004.9260 23.18303 -36.76543917 83.13151 -68.50024442 114.86631
## 2004.9288 23.64472 -36.39282001 83.68226 -68.17477315 115.46421
## 2004.9315 20.78873 -39.33774558 80.91520 -71.16677677 112.74423
## 2004.9342 22.33401 -37.88126691 82.54928 -69.75730662 114.42532
## 2004.9370 22.45518 -37.84875956 82.75913 -69.77173857 114.68211
## 2004.9397 23.90995 -36.48253323 84.30243 -68.45238262 116.27228
## 2004.9425 23.64067 -36.84022311 84.12156 -68.85687426 116.13822
## 2004.9452 21.31118 -39.25799821 81.88035 -71.32138281 113.94374
## 2004.9479 21.61086 -39.04646952 82.26819 -71.15651956 114.37824
## 2004.9507 21.30156 -39.44379475 82.04691 -71.60044250 114.20356
## 2004.9534 20.28882 -40.54443294 81.12207 -72.74761097 113.32525
## 2004.9562 20.95629 -39.96473635 81.87731 -72.21437754 114.12695
## 2004.9589 21.13757 -39.87109998 82.14623 -72.16713748 114.44227
## 2004.9616 20.04842 -41.04776816 81.14460 -73.39013540 113.48697
## 2004.9644 18.73040 -42.45317600 79.91398 -74.84180673 112.30261
## 2004.9671 16.53958 -44.73127370 77.81042 -77.16610192 110.24525
## 2004.9699 17.33594 -44.02204940 78.69394 -76.50300940 111.17490
## 2004.9726 17.47624 -43.96877830 78.92125 -76.49580466 111.44828
## 2004.9753 20.61486 -40.91705770 82.14677 -73.49008527 114.71980
## 2004.9781 21.01791 -40.60078415 82.63660 -73.21974805 115.25556
## 2004.9808 21.36981 -40.33553286 83.07515 -73.00036850 115.73999
## 2004.9836 22.84619 -38.94568864 84.63806 -71.65633169 117.34871
## 2004.9863 20.07386 -41.80442468 81.95215 -74.56081108 114.70854
## 2004.9890 21.32119 -40.64339120 83.28576 -73.44545716 116.08783
## 2004.9918 21.08895 -40.96179715 83.13970 -73.80947914 115.98738
## 2004.9945 22.44464 -39.69215862 84.58144 -72.58539338 117.47468
## 2004.9973 23.88663 -38.33610286 86.10936 -71.27482740 119.04809
## 2005.0000 24.41530 -37.89324283 86.72385 -70.87739441 119.70800
## 2005.0027 23.64690 -38.74733864 86.04114 -71.77685479 119.07066
## 2005.0055 22.56934 -39.91048436 85.04915 -72.98530285 118.12397
## 2005.0082 21.33776 -41.22752399 83.90304 -74.34758286 117.02310
## 2005.0110 22.07243 -40.57819189 84.72306 -73.74342942 117.88830
## 2005.0137 20.91589 -41.81996321 83.65174 -75.03031794 116.86210
## 2005.0164 24.55218 -38.26878530 87.37315 -71.52419603 120.62856
## 2005.0192 21.65143 -41.25453362 84.55739 -74.55493938 117.85780
## 2005.0219 19.43034 -43.56050666 82.42119 -76.90584674 115.76653
## 2005.0247 24.41696 -38.65865289 87.49258 -72.04886682 120.88279
## 2005.0274 25.88847 -37.27180161 89.04874 -70.70682916 122.48377
## 2005.0301 26.02004 -37.22477222 89.26485 -70.70455341 122.74463
## 2005.0329 24.37379 -38.95544773 87.70303 -72.47992282 121.22751
## 2005.0356 22.24627 -41.16728469 85.65983 -74.73639417 119.22894
## 2005.0384 23.14929 -40.34847381 86.64705 -73.96215840 120.26073
## 2005.0411 22.54337 -41.03848908 86.12522 -74.69668976 119.78342
## 2005.0438 21.98502 -41.68081318 85.65086 -75.38347115 119.35352
## 2005.0466 22.87562 -40.87408619 86.62533 -74.62114289 120.37239
## 2005.0493 21.75903 -42.07443916 85.59250 -75.86583624 119.38390
## 2005.0521 20.15676 -43.76035580 84.07388 -77.59603516 117.90956
## 2005.0548 23.04116 -40.95950324 87.04182 -74.83940700 120.92172
## 2005.0575 24.01153 -40.07256325 88.09563 -73.99663376 122.01970
## 2005.0603 22.03129 -42.13612809 86.19871 -76.10430792 120.16689
## 2005.0630 23.25205 -40.99858747 87.50268 -75.01081942 121.51492
## 2005.0658 22.64902 -41.68472592 86.98276 -75.74095301 121.03899
## 2005.0685 21.70167 -42.71507149 86.11842 -76.81523696 120.21859
## 2005.0712 24.45815 -40.04148715 88.95779 -74.18553445 123.10184
## 2005.0740 27.08434 -37.49809231 91.66677 -71.68596512 125.85464
## 2005.0767 24.61971 -40.04540323 89.28482 -74.27704544 123.51646
## 2005.0795 22.56057 -42.18711863 87.30826 -76.46247435 121.58361
## 2005.0822 26.20633 -38.62383269 91.03649 -72.94284624 125.35550
## 2005.0849 27.16862 -37.74390796 92.08115 -72.10652386 126.44376
## 2005.0877 27.43497 -37.55982272 92.42976 -71.96598573 126.83592
## 2005.0904 26.50902 -38.56792613 91.58597 -73.01758120 126.03562
## 2005.0932 24.08115 -41.07785387 89.24015 -75.57094615 123.73324
## 2005.0959 21.82315 -43.41780670 87.06410 -77.95428157 121.60058
## 2005.0986 22.29209 -43.03071160 87.61489 -77.61051463 122.19470
## 2005.1014 22.35538 -43.04916730 87.75993 -77.67224428 122.38301
## 2005.1041 25.56391 -39.92228538 91.05010 -74.58858227 125.71640
## 2005.1068 26.88179 -38.68594484 92.44953 -73.39540783 127.15899
## 2005.1096 24.08666 -41.56251321 89.73584 -76.31508869 124.48842
## 2005.1123 24.97278 -40.75773823 90.70330 -75.55337278 125.49893
## 2005.1151 27.03969 -38.77206516 92.85145 -73.61070556 127.69009
## 2005.1178 26.98740 -38.90550008 92.88030 -73.78709331 127.76189
## 2005.1205 24.71339 -41.26055156 90.68732 -76.18504479 125.61182
## 2005.1233 24.44516 -41.60971389 90.50004 -76.57705448 125.46738
## 2005.1260 24.73349 -41.40222721 90.86921 -76.41236273 125.87935
## 2005.1288 23.06029 -43.15617195 89.27675 -78.20905016 124.32963
## 2005.1315 24.47462 -41.82248636 90.77173 -76.91805520 125.86730
## 2005.1342 22.49757 -43.88008572 88.87522 -79.01829331 124.01343
## 2005.1370 24.51444 -41.94365968 90.97255 -77.12445436 126.15334
## 2005.1397 25.71179 -40.82666531 92.25024 -76.04999558 127.47357
## 2005.1425 27.11878 -39.49992883 93.73749 -74.76574339 129.00330
## 2005.1452 28.42195 -38.27692234 95.12081 -73.58517007 130.42906
## 2005.1479 29.21361 -37.56532456 95.99253 -72.91595453 131.34316
## 2005.1507 28.66119 -38.19770706 95.52008 -73.59066850 130.91305
## 2005.1534 26.46251 -40.47625910 93.40127 -75.91150146 128.83652
## 2005.1562 25.81203 -41.20651050 92.83057 -76.68398339 128.30805
## 2005.1589 26.59567 -40.50255480 93.69389 -76.02220800 129.21354
## 2005.1616 27.09325 -40.08455820 94.27106 -75.64634169 129.83284
## 2005.1644 25.46691 -41.79038980 92.72421 -77.39425372 128.32807
## 2005.1671 28.32860 -39.00809863 95.66530 -74.65399330 131.31119
## 2005.1699 28.63396 -38.78204341 96.04996 -74.46991934 131.73784
## 2005.1726 27.89432 -39.60089480 95.38953 -75.33070265 131.11934
## 2005.1753 28.70350 -38.87083028 96.27783 -74.64252091 132.04952
## 2005.1781 26.77808 -40.87527644 94.43144 -76.68880087 130.24496
## 2005.1808 23.92485 -43.80744525 91.65714 -79.66275466 127.51245
## 2005.1836 24.61371 -43.19742642 92.42484 -79.09447218 128.32189
## 2005.1863 25.29568 -42.59420088 93.18557 -78.53293451 129.12430
## 2005.1890 26.98864 -40.97990361 94.95718 -76.96027682 130.93756
## 2005.1918 28.28190 -39.76521292 96.32901 -75.78717757 132.35097
## 2005.1945 27.40945 -40.71614142 95.53504 -76.77964955 131.59854
## 2005.1973 27.22046 -40.98351260 95.42444 -77.08851640 131.52944
## 2005.2000 27.09137 -41.19089801 95.37365 -77.33734986 131.52010
## 2005.2027 28.24861 -40.11187501 96.60909 -76.29972743 132.79694
## 2005.2055 29.24106 -39.19754277 97.67965 -75.42674844 133.90886
## 2005.2082 28.81009 -39.70654011 97.32672 -75.97705189 133.59723
## 2005.2110 27.27129 -41.32328109 95.86586 -77.63505199 132.17763
## 2005.2137 27.38372 -41.28869816 96.05614 -77.64168135 132.40912
## 2005.2164 28.66551 -40.08467781 97.41569 -76.47882663 133.80984
## 2005.2192 28.20447 -40.62338980 97.03233 -77.05865773 133.46760
## 2005.2219 28.48983 -40.41561804 97.39528 -76.89195873 133.87162
## 2005.2247 29.36313 -39.61981694 98.34608 -76.13718420 134.86345
## 2005.2274 28.66027 -40.40009309 97.72063 -76.95844088 134.27898
## 2005.2301 30.32187 -38.81582143 99.45956 -75.41510386 136.05884
## 2005.2329 29.89718 -39.31775207 99.11211 -75.95792341 135.75228
## 2005.2356 30.65006 -38.64202482 99.94215 -75.32303948 136.62316
## 2005.2384 31.04096 -38.32819418 100.41012 -75.05000674 137.13193
## 2005.2411 30.30644 -39.13970329 99.75257 -75.90226847 136.51514
## 2005.2438 30.78623 -38.73680392 100.30927 -75.54007659 137.11254
## 2005.2466 30.04913 -39.55072374 99.64898 -76.39465894 136.49291
## 2005.2493 31.30543 -38.37115049 100.98201 -75.25570339 137.86656
## 2005.2521 33.08384 -36.66938068 102.83707 -73.59450659 139.76219
## 2005.2548 32.61044 -37.21934385 102.44022 -74.18499824 139.40588
## 2005.2575 31.71915 -38.18710620 101.62541 -75.19324469 138.63155
## 2005.2603 31.39872 -38.58392905 101.38138 -75.63050740 138.42795
## 2005.2630 32.58777 -37.47119155 102.64673 -74.55816565 139.73371
## 2005.2658 32.74668 -37.38851298 102.88186 -74.51583889 140.00919
## 2005.2685 33.30654 -36.90479262 103.51787 -74.07242653 140.68550
## 2005.2712 31.93427 -38.35312546 102.22166 -75.56102371 139.42956
## 2005.2740 32.34723 -38.01614191 102.71060 -75.26426096 139.95872
## 2005.2767 31.07633 -39.36293645 101.51560 -76.65123293 138.80390
## 2005.2795 31.70973 -38.80535122 102.22482 -76.13378187 139.55325
## 2005.2822 33.52745 -37.06336839 104.11827 -74.43189012 141.48679
## 2005.2849 33.81631 -36.85016380 104.48278 -74.25873364 141.89135
## 2005.2877 34.71854 -36.02350709 105.46058 -73.47208222 142.90915
## 2005.2904 33.56265 -37.25488569 104.38018 -74.74342341 141.86872
## 2005.2932 32.95516 -37.93777925 103.84811 -75.46623700 141.37657
## 2005.2959 34.08581 -36.88246324 105.05409 -74.45079860 142.62242
## 2005.2986 33.28464 -37.75888389 104.32817 -75.36705459 141.93634
## 2005.3014 32.72647 -38.39222981 103.84516 -76.04019369 141.49313
## 2005.3041 34.08326 -37.11052775 105.27705 -74.79824280 142.96476
## 2005.3068 34.56281 -36.70598993 105.83161 -74.43341426 143.55904
## 2005.3096 35.08883 -36.25490811 106.43256 -74.02199997 144.19965
## 2005.3123 34.57873 -36.83985608 105.99732 -74.64657386 143.80404
## 2005.3151 33.94761 -37.54575369 105.44098 -75.39205589 143.28728
## 2005.3178 34.60379 -36.96427338 106.17186 -74.85011864 144.05770
## 2005.3205 34.34280 -37.29988558 105.98549 -75.22523268 143.91083
## 2005.3233 34.68704 -37.03019267 106.40427 -74.99500050 144.36907
## 2005.3260 35.33943 -36.45226416 107.13113 -74.45649175 145.13535
## 2005.3288 33.25109 -38.61499546 105.11717 -76.65860197 143.16078
## 2005.3315 33.65895 -38.28144475 105.59935 -76.36438946 143.68229
## 2005.3342 34.75022 -37.26440823 106.76485 -75.38665054 144.88709
## 2005.3370 35.56147 -36.52732032 107.65026 -74.68881976 145.81176
## 2005.3397 33.69237 -38.47050410 105.85524 -76.67122033 144.05595
## 2005.3425 33.32458 -38.91229558 105.56146 -77.15218839 143.80135
## 2005.3452 33.92187 -38.38893733 106.23268 -76.66796662 144.51171
## 2005.3479 34.42248 -37.96218437 106.80714 -76.28031017 145.12527
## 2005.3507 36.00486 -36.45358713 108.46330 -74.81076958 146.82048
## 2005.3534 35.44893 -37.08321395 107.98108 -75.47941333 146.37728
## 2005.3562 36.04645 -36.55932673 108.65223 -74.99450343 147.08740
## 2005.3589 36.30524 -36.37408877 108.98458 -74.84820330 147.45869
## 2005.3616 35.72844 -37.02436902 108.48126 -75.53738202 146.99427
## 2005.3644 35.00293 -37.82329250 107.82915 -76.37516472 146.38102
## 2005.3671 35.79269 -37.10686532 108.69224 -75.69755762 147.28293
## 2005.3699 35.98889 -36.98391792 108.96171 -75.61339130 147.59118
## 2005.3726 35.91186 -37.13413420 108.95786 -75.80234976 147.62608
## 2005.3753 37.14052 -35.97858834 110.25963 -74.68550731 148.96655
## 2005.3781 35.88988 -37.30227272 109.08203 -76.04785643 147.82761
## 2005.3808 36.51058 -36.75453899 109.77569 -75.53874890 148.55990
## 2005.3836 37.04571 -36.29230522 110.38372 -75.11510290 149.20651
## 2005.3863 37.03063 -36.38019940 110.44147 -75.24154653 149.30281
## 2005.3890 36.23782 -37.24576409 109.72140 -76.14562247 148.62126
## 2005.3918 34.78053 -38.77573225 108.33679 -77.71406379 147.27512
## 2005.3945 35.16981 -38.45905301 108.79868 -77.43581973 147.77544
## 2005.3973 35.17821 -38.52318583 108.87961 -77.53834987 147.89478
## 2005.4000 36.17215 -37.60171695 109.94601 -76.65524056 148.99953
## 2005.4027 35.34017 -38.50608614 109.18642 -77.59793168 148.27827
## 2005.4055 37.02464 -36.89393583 110.94321 -76.02406577 150.07334
## 2005.4082 37.58937 -36.40145118 111.58020 -75.56982810 150.74858
## 2005.4110 37.88535 -36.17765153 111.94836 -75.38423811 151.15495
## 2005.4137 37.89229 -36.24282284 112.02741 -75.48758188 151.27217
## 2005.4164 38.08892 -36.11823613 112.29607 -75.40113055 151.57897
## 2005.4192 36.79556 -37.48356735 111.07468 -76.80456015 150.39567
## 2005.4219 37.00514 -37.34588743 111.35616 -76.70494174 150.71521
## 2005.4247 35.84085 -38.58200626 110.26370 -77.97908530 149.66078
## 2005.4274 35.85676 -38.63785446 110.35138 -78.07292158 149.78644
## 2005.4301 36.22227 -38.34403236 110.78858 -77.81705099 150.26160
## 2005.4329 36.00510 -38.63283204 110.64303 -78.14376573 150.15396
## 2005.4356 37.19863 -37.51085239 111.90812 -77.05966479 151.45693
## 2005.4384 36.94062 -37.84035251 111.72159 -77.42700737 151.30824
## 2005.4411 37.36744 -37.48495276 112.21983 -77.10941395 151.84429
## 2005.4438 36.09036 -38.83337682 111.01410 -78.49560829 150.67633
## 2005.4466 35.88632 -39.10869601 110.88135 -78.80866183 150.58131
## 2005.4493 36.72876 -38.33747966 111.79499 -78.07514401 151.53265
## 2005.4521 37.34582 -37.79156636 112.48320 -77.56689350 152.25852
## 2005.4548 36.14395 -39.06451050 111.35241 -78.87746480 151.16537
## 2005.4575 35.84355 -39.43592481 111.12302 -79.28647074 150.97357
## 2005.4603 36.94056 -38.40985663 112.29098 -78.29795877 152.17908
## 2005.4630 36.07806 -39.34323646 111.49936 -79.26885948 151.42498
## 2005.4658 36.46989 -39.02221813 111.96200 -78.98532680 151.92511
## 2005.4685 37.07900 -38.48385322 112.64186 -78.48441241 152.64242
## 2005.4712 37.10515 -38.52838949 112.73868 -78.56636417 152.77665
## 2005.4740 37.39795 -38.30619704 113.10210 -78.38155228 153.17745
## 2005.4767 36.95492 -38.81977091 112.72962 -78.93247188 152.84232
## 2005.4795 37.27445 -38.57072465 113.11963 -78.72073661 153.26964
## 2005.4822 38.26726 -37.64833557 114.18285 -77.83562388 154.37014
## 2005.4849 37.79162 -38.19432555 113.77757 -78.41885566 154.00210
## 2005.4877 37.15979 -38.89644021 113.21602 -79.15817768 153.47776
## 2005.4904 37.91082 -38.21563834 114.03727 -78.51454881 154.33618
## 2005.4932 38.99040 -37.20621482 115.18701 -77.54226404 155.52306
## 2005.4959 39.05072 -37.21598420 115.31742 -77.58913800 155.69058
## 2005.4986 37.39602 -38.94070719 113.73275 -79.35093150 154.14298
## 2005.5014 37.62844 -38.77825499 114.03513 -79.22551583 154.48239
## 2005.5041 38.27069 -38.20589963 114.74729 -78.69016313 155.23155
## 2005.5068 37.46640 -39.08002747 114.01283 -79.60125984 154.53406
## 2005.5096 37.65882 -38.95737799 114.27503 -79.51554552 154.83319
## 2005.5123 38.54743 -38.13847780 115.23334 -78.73354689 155.82841
## 2005.5151 38.58190 -38.17365800 115.33745 -78.80559514 155.96939
## 2005.5178 38.66628 -38.15885391 115.49142 -78.82762568 156.16020
## 2005.5205 38.10379 -38.79087192 114.99844 -79.49644498 155.70402
## 2005.5233 38.99478 -37.96932946 115.95890 -78.71167057 156.70124
## 2005.5260 38.48007 -38.55344319 115.51357 -79.33251920 156.29265
## 2005.5288 37.93729 -39.16555217 115.04013 -79.98133002 155.85591
## 2005.5315 37.79885 -39.37325763 114.97096 -80.22570435 155.82341
## 2005.5342 37.30115 -39.94017036 114.54246 -80.82925306 155.43154
## 2005.5370 38.17304 -39.13742032 115.48350 -80.06310621 156.40919
## 2005.5397 38.72999 -38.64955003 116.10954 -79.61180639 157.07179
## 2005.5425 38.74992 -38.69864699 116.19848 -79.69744121 157.19728
## 2005.5452 37.73859 -39.77893804 115.25611 -80.81423758 156.29141
## 2005.5479 38.25482 -39.33160898 115.84124 -80.40338140 156.91301
## 2005.5507 37.44424 -40.21102733 115.09950 -81.31924027 156.20771
## 2005.5534 37.38363 -40.34040467 115.10767 -81.48502585 156.25230
## 2005.5562 37.20438 -40.58837877 114.99713 -81.76937601 156.17813
## 2005.5589 38.37489 -39.48652097 116.23630 -80.70386216 157.45364
## 2005.5616 38.50570 -39.42430376 116.43571 -80.67795688 157.68936
## 2005.5644 37.57373 -40.42480753 115.57227 -81.71474065 156.86221
## 2005.5671 38.29604 -39.77097200 116.36306 -81.09715327 157.68924
## 2005.5699 38.59821 -39.53722148 116.73364 -80.89961913 158.09603
## 2005.5726 38.57277 -39.63101435 116.77655 -81.02959670 158.17514
## 2005.5753 38.95516 -39.31692016 117.22724 -80.75165561 158.66197
## 2005.5781 38.77285 -39.56746399 117.11316 -81.03832102 158.58402
## 2005.5808 37.47278 -40.93570586 115.88127 -82.44265304 157.38822
## 2005.5836 37.80941 -40.66719568 116.28602 -82.21020165 157.82902
## 2005.5863 38.07499 -40.46967085 116.61966 -82.04870434 158.19869
## 2005.5890 38.72859 -39.88407047 117.34125 -81.49910030 158.95628
## 2005.5918 38.32938 -40.35122053 117.00998 -82.00221558 158.66098
## 2005.5945 38.52241 -40.22607613 117.27089 -81.91300537 158.95782
## 2005.5973 38.24781 -40.56850075 117.06411 -82.29133324 158.78695
## 2005.6000 38.93087 -39.95320108 117.81494 -81.71190595 159.57365
## 2005.6027 37.08008 -41.87169336 116.03186 -83.66623981 157.82641
## 2005.6055 35.98888 -43.03054120 115.00831 -84.86089853 156.83867
## 2005.6082 35.53528 -43.55173422 114.62230 -85.41787179 156.48844
## 2005.6110 35.90615 -43.24839465 115.06070 -85.15028192 156.96259
## 2005.6137 37.25580 -41.96622267 116.47783 -83.90382916 158.41543
## 2005.6164 37.52158 -41.76785735 116.81103 -83.74115266 158.78432
## 2005.6192 36.92394 -42.43286141 116.28074 -84.44181522 158.28970
## 2005.6219 35.27526 -44.14884470 114.69937 -86.19342677 156.74395
## 2005.6247 34.93507 -44.55628653 114.42642 -86.63646669 156.50660
## 2005.6274 36.29109 -43.26745623 115.84963 -85.38320440 157.96538
## 2005.6301 36.40665 -43.21902825 116.03232 -85.37031441 158.18361
## 2005.6329 36.14076 -43.55199582 115.83351 -85.73879004 158.02030
## 2005.6356 36.89777 -42.86200474 116.65754 -85.08427714 158.87981
## 2005.6384 36.57974 -43.24699545 116.40647 -85.50471626 158.66420
## 2005.6411 37.63636 -42.25728155 117.53000 -84.55042107 159.82314
## 2005.6438 37.81953 -42.14096465 117.78002 -84.46949322 160.10855
## 2005.6466 36.71302 -43.31426715 116.74031 -85.67815522 159.10420
## 2005.6493 36.32287 -43.77115935 116.41690 -86.17037743 158.81612
## 2005.6521 36.04087 -44.11984330 116.20158 -86.55436197 158.63610
## 2005.6548 34.90720 -45.32014359 115.13454 -87.78993351 157.60433
## 2005.6575 35.29591 -44.99800468 115.58983 -87.50303658 158.09486
## 2005.6603 34.90530 -45.45513936 115.26573 -87.99538405 157.80598
## 2005.6630 34.53673 -45.89016511 114.96363 -88.46559346 157.53906
## 2005.6658 34.72782 -45.76549216 115.22112 -88.37607513 157.83171
## 2005.6685 35.39459 -45.16507351 115.95425 -87.81078211 158.59996
## 2005.6712 35.64422 -44.98173622 116.27018 -87.66254154 158.95099
## 2005.6740 35.40171 -45.29049524 116.09392 -88.00636845 158.80979
## 2005.6767 34.11592 -46.64247901 114.87431 -89.39339133 157.62522
## 2005.6795 35.10043 -45.72410059 115.92496 -88.51002335 158.71089
## 2005.6822 35.30470 -45.58591678 116.19531 -88.40682134 159.01622
## 2005.6849 35.36310 -45.59354682 116.31974 -88.44940462 159.17560
## 2005.6877 33.27493 -47.74768237 114.29755 -90.63846494 157.18833
## 2005.6904 33.36470 -47.72384128 114.45323 -90.64952020 157.37891
## 2005.6932 32.42228 -48.73212016 113.57669 -91.69266708 156.53724
## 2005.6959 32.80239 -48.41783190 114.02261 -91.41321855 157.01799
## 2005.6986 31.29048 -49.99550212 112.57646 -93.02570029 155.60665
## 2005.7014 32.10386 -49.24782526 113.45555 -92.31280681 156.52053
## 2005.7041 32.82214 -48.59519618 114.23949 -91.69493303 157.33922
## 2005.7068 32.79602 -48.68692208 114.27896 -91.82138623 157.41343
## 2005.7096 32.64115 -48.90733975 114.18964 -92.07650327 157.35881
## 2005.7123 31.83624 -49.77774333 113.45023 -92.98157835 156.65407
## 2005.7151 32.26565 -49.41378516 113.94508 -92.65226387 157.18355
## 2005.7178 33.52658 -48.21823950 115.27140 -91.49133417 158.54450
## 2005.7205 33.56537 -48.24479072 115.37553 -91.55247368 158.68321
## 2005.7233 33.47551 -48.39993304 115.35096 -91.74217670 158.69321
## 2005.7260 33.41300 -48.52767857 115.35369 -91.90445538 158.73046
## 2005.7288 30.62072 -51.38514841 112.62658 -94.79643090 156.03786
## 2005.7315 30.19323 -51.87776127 112.26423 -95.32352204 155.70999
## 2005.7342 30.18195 -51.95412949 112.31802 -95.43434119 155.79823
## 2005.7370 29.55750 -52.64360345 111.75860 -96.15823881 155.27324
## 2005.7397 31.34930 -50.91678116 113.61538 -94.46581298 157.16441
## 2005.7425 32.07855 -50.25245435 114.40955 -93.83585547 157.99296
## 2005.7452 33.08041 -49.31546403 115.47629 -92.93320738 159.09404
## 2005.7479 32.90438 -49.55632516 115.36508 -93.20838371 159.01714
## 2005.7507 32.97420 -49.55127529 115.49967 -93.23762209 159.18602
## 2005.7534 32.59299 -49.99720419 115.18319 -93.71781235 158.90379
## 2005.7562 30.89193 -51.76293696 113.54679 -95.51777965 157.30164
## 2005.7589 29.06668 -53.65280544 111.78617 -97.44185590 155.57522
## 2005.7616 27.82460 -54.95944997 110.60866 -98.78268149 154.43189
## 2005.7644 29.49235 -53.35622535 112.34092 -97.21361130 156.19831
## 2005.7671 30.61111 -52.30193385 113.52415 -96.19344765 157.41567
## 2005.7699 31.43556 -51.54190031 114.41302 -95.46751544 158.33864
## 2005.7726 32.41830 -50.62353424 115.46013 -94.58322425 159.41982
## 2005.7753 32.49348 -50.61266554 115.59964 -94.60640404 159.59337
## 2005.7781 32.00232 -51.16809842 115.17274 -95.19585907 159.20050
## 2005.7808 30.64694 -52.58769888 113.88158 -96.64945542 157.94334
## 2005.7836 30.68177 -52.61704325 113.98058 -96.71276947 158.07630
## 2005.7863 30.74598 -52.61694814 114.10891 -96.74661789 158.23858
## 2005.7890 28.20937 -55.21762928 111.63637 -99.38121646 155.79996
## 2005.7918 27.97080 -55.52022593 111.46182 -99.71770453 155.65930
## 2005.7945 28.74415 -54.81084721 112.29915 -99.04219125 156.53049
## 2005.7973 28.98285 -54.63607480 112.60177 -98.90125837 156.86695
## 2005.8000 30.53876 -53.14404152 114.22155 -97.44303878 158.52055
## 2005.8027 31.08754 -52.65908350 114.83417 -96.99186864 159.16695
## 2005.8055 30.40679 -53.40361624 114.21719 -97.77016355 158.58374
## 2005.8082 29.89525 -53.97887945 113.76939 -98.37916324 158.16967
## 2005.8110 29.66012 -54.27769027 113.59794 -98.71168494 158.03193
## 2005.8137 30.53320 -53.46824479 114.53465 -97.93592478 159.00233
## 2005.8164 29.17009 -54.89493914 113.23512 -99.39627895 157.73646
## 2005.8192 28.24376 -55.88480459 112.37233 -100.41977878 156.90731
## 2005.8219 27.29625 -56.89580994 111.48831 -101.46439312 156.05689
## 2005.8247 28.10239 -56.15311146 112.35789 -100.75527832 156.96005
## 2005.8274 28.14285 -56.17604087 112.46174 -100.81176613 157.09747
## 2005.8301 29.10980 -55.27243447 113.49204 -99.94169292 158.16130
## 2005.8329 26.81817 -57.62736544 111.26371 -102.33013193 155.96647
## 2005.8356 25.08926 -59.41952652 109.59805 -104.15577595 154.33430
## 2005.8384 27.16000 -57.41199326 111.73199 -102.18170058 156.50169
## 2005.8411 28.63714 -55.99800458 113.27229 -100.80114482 158.07543
## 2005.8438 27.33552 -57.36273676 112.03377 -102.19928498 156.87032
## 2005.8466 24.49701 -60.26430443 109.25833 -105.13423576 154.12826
## 2005.8493 25.26265 -59.56167969 110.08699 -104.46496931 154.99028
## 2005.8521 25.11165 -59.77564684 109.99896 -104.71226998 154.93558
## 2005.8548 25.35216 -59.59806382 110.30238 -104.56799578 155.27232
## 2005.8575 26.19308 -58.82001560 111.20618 -103.82323173 156.20940
## 2005.8603 29.20590 -55.87002631 114.28183 -100.90650201 159.31830
## 2005.8630 26.40150 -58.73720749 111.54021 -103.80691821 156.60992
## 2005.8658 24.21487 -60.98657361 109.41632 -106.08949486 154.51924
## 2005.8685 25.53978 -59.72435567 110.80392 -104.86046303 155.94002
## 2005.8712 26.85189 -58.47488905 112.17867 -103.64415811 157.34794
## 2005.8740 24.90127 -60.48811124 110.29065 -105.69051769 155.49305
## 2005.8767 23.90887 -61.54306267 109.36080 -106.77858224 154.59632
## 2005.8795 23.80878 -61.70566087 109.32321 -106.97426932 154.59182
## 2005.8822 25.05204 -60.52486229 110.62893 -105.82653547 155.93061
## 2005.8849 23.43831 -62.20099985 109.07763 -107.53571363 154.41234
## 2005.8877 23.76433 -61.93735296 109.46601 -107.30508329 154.83374
## 2005.8904 25.34406 -60.41995116 111.10806 -105.82067402 156.50879
## 2005.8932 26.28641 -59.53987656 112.11270 -104.97356800 157.54639
## 2005.8959 24.99060 -60.89791863 110.87912 -106.36455474 156.34576
## 2005.8986 25.35943 -60.59127440 111.31014 -106.09083132 156.80970
## 2005.9014 26.16791 -59.84494222 112.18076 -105.37739615 157.71322
## 2005.9041 24.76349 -61.31146062 110.83844 -106.87678781 156.40377
## 2005.9068 25.16508 -60.97192259 111.30209 -106.57009935 156.90027
## 2005.9096 27.95376 -58.24525420 114.15278 -103.87625687 159.78378
## 2005.9123 25.43331 -60.82767496 111.69429 -106.49147994 157.35809
## 2005.9151 23.22653 -63.09636761 109.54944 -108.79295137 155.24602
## 2005.9178 23.51102 -62.87375722 109.89580 -108.60309625 155.62514
## 2005.9205 22.96464 -63.48196476 109.41125 -109.24403561 155.17333
## 2005.9233 24.85602 -61.65237292 111.36442 -107.44715221 157.15920
## 2005.9260 23.18303 -63.38710598 109.75318 -109.21457036 155.58064
## 2005.9288 23.64472 -62.98712193 110.27656 -108.84724811 156.13669
## 2005.9315 20.78873 -65.90477063 107.48222 -111.79753535 153.37499
## 2005.9342 22.33401 -64.42110261 109.08911 -110.34648269 155.01449
## 2005.9370 22.45518 -64.36149297 109.27186 -110.31946525 155.22983
## 2005.9397 23.90995 -62.96825089 110.78815 -108.95879228 156.77869
## 2005.9425 23.64067 -63.29901110 110.58035 -109.32209855 156.60344
## 2005.9452 21.31118 -65.68994214 108.31230 -111.74555266 154.36791
## 2005.9479 21.61086 -65.45165452 108.67337 -111.53976514 154.76148
## 2005.9507 21.30156 -65.82230549 108.42542 -111.94289332 154.54601
## 2005.9534 20.28882 -66.89635360 107.47399 -113.04939579 153.62703
## 2005.9562 20.95629 -66.29015069 108.20272 -112.47562442 154.38820
## 2005.9589 21.13757 -66.17009127 108.44523 -112.38797380 154.66311
## 2005.9616 20.04842 -67.32041923 107.41726 -113.57068784 153.66752
## 2005.9644 18.73040 -68.69956924 106.16038 -114.98220127 152.44301
## 2005.9671 16.53958 -70.95149103 104.03064 -117.26646387 150.34561
## 2005.9699 17.33594 -70.21617233 104.88806 -116.56346341 151.23535
## 2005.9726 17.47624 -70.13688787 105.08936 -116.51647466 151.46895
## 2005.9753 20.61486 -67.05923453 108.28895 -113.47109457 154.70081
## 2005.9781 21.01791 -66.71710842 108.75292 -113.16121928 155.19703
## 2005.9808 21.36981 -66.42608434 109.16571 -112.90242364 155.64204
## 2005.9836 22.84619 -65.01054665 110.70292 -111.51909206 157.21147
## 2005.9863 20.07386 -67.84366814 107.99139 -114.38439737 154.53212
## 2005.9890 21.32119 -66.65709859 109.29947 -113.22998940 155.87236
## 2005.9918 21.08895 -66.95004654 109.12795 -113.55507674 155.73298
## 2005.9945 22.44464 -65.65502767 110.54431 -112.29217511 157.18146
## 2005.9973 23.88663 -64.27366883 112.04693 -110.94291140 158.71617
## 2006.0000 24.41530 -63.80558256 112.63619 -110.50689821 159.33750
## 2006.0027 23.64690 -64.63452859 111.92833 -111.36789530 158.66170
## 2006.0055 22.56934 -65.77260055 110.91127 -112.53799637 157.67667NOTE: AIC = 21549.73 , BIC = 21566.81 , RMSE = 2.902054
Also, the headline of the plot below contains STL + ETS(A,N,N) showing that the automated model characterized error of the “tsT_PK” SERIES as Additative (A), trend as None (A) and seasonality as None (N) which is equivalent to simple exponential model(ses) with only alpha parameter i.e level.
#Model 2 : ARIMA Model It is used for forecasting for both seasonal and non- seasonal level.
#Changing to stationary set
train.sta1 <- diff(train1, diff =2)
test.sta1 <- diff(test1, diff =2)2.1 Auto Arima model without sesonality:
set.seed(301)
model_VAR2 <- auto.arima(train.sta1, seasonal = FALSE)
summary(model_VAR2)## Series: train.sta1
## ARIMA(1,0,3) with non-zero mean
##
## Coefficients:
## ar1 ma1 ma2 ma3 mean
## 0.4847 -1.7074 0.5080 0.2024 0e+00
## s.e. 0.0331 0.0342 0.0617 0.0285 4e-04
##
## sigma^2 estimated as 8.919: log likelihood=-5507.16
## AIC=11026.31 AICc=11026.35 BIC=11060.46
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 0.0004542817 2.983101 2.070462 NaN Inf 0.4204283 0.01071112NOTE: AIC = 11026.31 , BIC = 11060.46 , RMSE =2.983101
tsdisplay(residuals(model_VAR2), lag.max = 45, main = '(1,1,1) Model Residuals')
#2.2 Auto Arima model with sesonality:
set.seed(301)
model2_VAR2 <- auto.arima(train.sta1, seasonal= TRUE)
summary(model2_VAR2)## Series: train.sta1
## ARIMA(5,0,0) with zero mean
##
## Coefficients:
## ar1 ar2 ar3 ar4 ar5
## -0.8365 -0.7683 -0.6262 -0.4388 -0.1951
## s.e. 0.0210 0.0259 0.0276 0.0259 0.0210
##
## sigma^2 estimated as 12.74: log likelihood=-5894.48
## AIC=11800.97 AICc=11801 BIC=11835.12
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 0.0005491905 3.564718 2.401756 NaN Inf 0.4877009 -0.04422588NOTE: AIC = 11800.97 , BIC = 11835.12 , RMSE =3.564718
tsdisplay(residuals(model2_VAR2), lag.max = 20, main = 'Seasonal Model Residuals')
NOTE: Above Graphs shows serious lags at 5, so modify model for p or q = 5
#2.3 Manual Arima
Passing parameter order = (1,0,5) which means p(member of lags of a variable to be used as a predictor) = 1, d = 0(members of differences needed for stationarity) and q = 5 (moving average order - number of lagged forecasts error in the prediction equation)
set.seed(301)
model1_VAR2 <- arima(train.sta1, order = c(1,0,5))
summary(model1_VAR2)##
## Call:
## arima(x = train.sta1, order = c(1, 0, 5))
##
## Coefficients:
## ar1 ma1 ma2 ma3 ma4 ma5 intercept
## -0.0608 -1.1492 -0.1639 0.1007 0.1046 0.1133 0e+00
## s.e. 0.2824 0.2810 0.3490 0.0430 0.0517 0.0600 3e-04
##
## sigma^2 estimated as 8.885: log likelihood = -5505.47, aic = 11026.94
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 0.002088656 2.980804 2.069952 NaN Inf 0.3813413 -0.0001374768NOTE: AIC = 11026.94, RMSE =2.980804
tsdisplay(residuals(model1_VAR2), lag.max = 20, main = 'Seasonal Model Residuals')
#Visualising forecast by each model
par(mfrow = c(2,2))
fit_auto_train_VAR2 %>% forecast(h=341) %>% autoplot() + autolayer(test1) 
model1_VAR2 %>% forecast(h=341) %>% autoplot() 
model2_VAR2 %>% forecast(h=341) %>% autoplot() 
model_VAR2 %>% forecast(h=341) %>% autoplot() 
Plot and comment on the residuals of the fitted data for both models in the same plot.
Residual Plot - to confirm no problem with this model
par(mfrow= c(2,2))
hist(fit_auto_train_VAR2$residuals,col = 'red',xlab = 'Error',main = 'Histogram Of Residuals',freq= FALSE)
lines(density(fit_auto_train_VAR2$residuals))
hist(model_VAR2$residuals,col = 'red',xlab = 'Error',main = 'Histogram Of Residuals',freq= FALSE)
lines(density(model_VAR2$residuals))
hist(model1_VAR2$residuals,col = 'red',xlab = 'Error',main = 'Histogram Of Residuals',freq= FALSE)
lines(density(model1_VAR2$residuals))
hist(model2$residuals,col = 'red',xlab = 'Error',main = 'Histogram Of Residuals',freq= FALSE)
lines(density(model2_VAR2$residuals))
OBSERVATION: The residuals for each model are normally distributed, which shows the good fit of the models. It is normally distrbuted.
Testing the autocorrelation and partial autocorrelation of the residuals (using the plots and Ljung-Box Q statistic) up to an appropriate lag *
- ACF & PACF Plots
par(mfrow = c(2,2))
acf(fit_auto_train_VAR2$residuals, main = 'Correlogram')
acf(model_VAR2$residuals, main = 'Correlogram')
acf(model1_VAR2$residuals, main = 'Correlogram')
acf(model2_VAR2$residuals, main = 'Correlogram')
#PACF PLOTS
par(mfrow = c(2,2))
pacf(fit_auto_train_VAR2$residuals, main = 'Partial Corelogram')
pacf(model_VAR2$residuals, main = 'Partial Corelogram')
pacf(model1_VAR2$residuals, main = 'Partial Corelogram')
pacf(model2_VAR2$residuals, main = 'Partial Corelogram')
NOTE: 1. Residuals are the difference between actaual and fitted values
2. These blue lines are signficance bounds
3. This graph shows us the autocorelations for insample forecast errors
4. Do not exceed these significance bounds for lags 1 to end
- Ljunx-Box Test to check the autocorelations of the residuals
This test used to test the lack of fit of a time series model.
This test is applied to the residuals of the time series model
We reject the null hypothesis, if p value is less than 0.05. This test is generally done for ARIMA models
#Ljunx-Box Test to check the autocorelations of the residuals
Box.test(model_VAR2$residuals, lag =20, type = 'Ljung-Box')##
## Box-Ljung test
##
## data: model_VAR2$residuals
## X-squared = 46.055, df = 20, p-value = 0.0007922Box.test(model1_VAR2$residuals, lag =20, type = 'Ljung-Box')##
## Box-Ljung test
##
## data: model1_VAR2$residuals
## X-squared = 39.927, df = 20, p-value = 0.005103Box.test(model2_VAR2$residuals, lag =20, type = 'Ljung-Box')##
## Box-Ljung test
##
## data: model2_VAR2$residuals
## X-squared = 261.08, df = 20, p-value < 2.2e-16OBSERVATIONS:
For above performed Ljunx-Box Test on model_VAR2,model1_VAR2 and model2_VAR2 output, we can say that p-value is less than significance level 0.05, then there is a statistical significance.
We conclude that there is a liitle evidence of non-zero auto-corelations in the insample forecast errors at lags 1 to 20.
So we rejects the null hypothesis. Hence, we conclude that there is serial auto corelation present between lags.
Validating The Model by testing the model performance with Holdout set
Here, choosing RMSE as evaluation parameter. The lower RMSE indicates a more accurate forecast.
Below, is the comparison of model. We are fitting the model to test set which is the holdout set. And checking the accuracy using RMSE(Root mean square error) evaluation parameter.
accuracy(forecast(fit_auto_train_VAR2), test1) ["Test set", "RMSE"]## [1] 6.771375#o/p - 6.771375accuracy(forecast(model1_VAR2), test.sta1) ["Test set", "RMSE"]## [1] 4.442126#O/P - 4.442126accuracy(forecast(model2_VAR2), test.sta1) ["Test set", "RMSE"]## [1] 4.453695#o/p - 4.453695accuracy(forecast(model_VAR2), test.sta1) ["Test set", "RMSE"]## [1] 4.44153#O/P - 4.44153NOTE:- Here, the RMSE value is less of ARIMA models compared to exponential model.
The minimum RMSE is of model1_VAR2.
The RMSE of auto arima models with seasonality and without seasonality have little difference.
COMMENT ON BEST MODEL AND ITS PARAMETERS We observed the best model to be ARIMA model i.e.“model1_VAR2”.
summary(model1_VAR2)##
## Call:
## arima(x = train.sta1, order = c(1, 0, 5))
##
## Coefficients:
## ar1 ma1 ma2 ma3 ma4 ma5 intercept
## -0.0608 -1.1492 -0.1639 0.1007 0.1046 0.1133 0e+00
## s.e. 0.2824 0.2810 0.3490 0.0430 0.0517 0.0600 3e-04
##
## sigma^2 estimated as 8.885: log likelihood = -5505.47, aic = 11026.94
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 0.002088656 2.980804 2.069952 NaN Inf 0.3813413 -0.0001374768Passing parameter order = (1,0,5) ,which means
p = 1,
d = 0
q = 5
For the best model, 1 member of lag is used as a predictor. As we transformed the series to stationary so members of differences needed for stationarity is 0. 5 are the number of lagged forecasts errors used in the prediction equation.
AIC = 11026.94, RMSE = 2.980804 which is minimum as compared to other models
3. Forecasting on Average T (T_AV)
#Checking the attributes of time series
attributes(tsT_AV)## $tsp
## [1] 1998.00 2004.94 365.00
##
## $class
## [1] "ts"Plotting the series
plot(tsT_AV, main = "Average T observed for years (tsT_AV)", ylim = c(0,35), col = "red")
From the plot, we observes that there is no trend but seems to have seasonlity.
Most of the data is missing for year 2002 to 2003 .
Checking the statistics and visualising the missing data in the series:
plotNA.distribution(tsT_AV)
As we see there is a large gap in the missing data, so locf and NOCB would not seems the good technique to implement here.
Also, as no trend is being observed here, so not necessary to use “Kalman filter with arima state space model” as it works best for series having trend and seasonality.
Hence, using “Linear interpolation” technique to impute missing values. This method works good for series having seasonality but no trend type of time series data.
#Impute the missing values with “na_interpolation” function of “imputeTS package” and visualise the imputed values in the time series
tsT_AV.imp <- na_interpolation(tsT_AV, method = "linear")
plotNA.imputations(tsT_AV, tsT_AV.imp)
#Decomposition Of Time Series
decomp2 <- decompose(tsT_AV.imp)
plot(decomp2, col = "red")
OBSERVATIONS:
1)There seems to have trend and seasonality both
2)From 1998 to 2001 seems to have downward trend and from 2001 to 2005 seems to have upward trend.
3)We observe some seasonality in the series. Means there is some seasonality. Seasonality describes cyclical effects due to the time of the year.
Let’s explore this seasonality pattern by plotting the decomp$seasonal components such that y-axis represents Seasonality Index and x-axis has month
#Visualising the seasonal data
par(mfrow= c(1,2))
plot(decomp2$seasonal, type ='b', xlab = 'Years', ylab = 'Seasonality Index', col = 'blue', las = 2, main = "SEASONAL DATA")
plot(decomp2$seasonal[1:400], type ='b', xlab = 'Years', ylab = 'Seasonality Index', col = 'blue', las = 2, main = "SEASONAL DATA")
OBSERVATIONS:
1) There is increase in the mid of months of a year.
2) There is a drop in peak T for starting and ending months of the year
#Stationarity check of time series
We could check the stationarity of time series by ADF and KPSS Tests:
- Augmented Dickey- Fuller(ADF) t-statistic test for unit root
- Kwiatkowski-Phillips-Schmidt-Shin (KPSS) for level or trend stationarity
adf.test(tsT_AV.imp)##
## Augmented Dickey-Fuller Test
##
## data: tsT_AV.imp
## Dickey-Fuller = -3.7095, Lag order = 13, p-value = 0.02351
## alternative hypothesis: stationary#p-value is less than 0.05, hence it is stationary
kpss.test(tsT_AV.imp, null="Trend")##
## KPSS Test for Trend Stationarity
##
## data: tsT_AV.imp
## KPSS Trend = 0.19928, Truncation lag parameter = 8, p-value = 0.01627#p-value is less than 0.05, hence it is not trend- stationaryNOTE: From the both tests results, it leads to CASE4, we could recheck by visualising it i.e. by plotting ACF. Second, we can check each for characteristics of stationarity by looking at the autocorrelation functions (ACF) of each signal. For a stationary signal, because we expect no dependence with time, we would expect the ACF to go to 0 for each time lag (τ). Lets visualize the signals and ACFs.
acf(tsT_AV.imp,lag.max = length(tsT_AV.imp),xlab = "lag #", ylab = 'ACF',main='Statiionary Check ')
It seems difference of 1 is sufficient to make the series stationary.
tsT_AV.sta <- diff(tsT_AV.imp, diff =1)
acf(tsT_AV.sta, lag.max = length(tsT_AV.sta),xlab = "lag #", ylab = 'ACF',main='Statiionary Check ')
Hence, after differencing our series is now transformed to stationary time series.
#Visualising the stationary series
plot(tsT_AV.sta, col = "red", main = "Stationary Series")
#CREATING MODELS AND FORECASTING: USING EXPONENTIAL SMOOTHING AND ARIMA TECHNIQUES FOR TIME SERIES FORECASTING
1.Train - Test Split of the data
train2 <- window(tsT_AV.imp, end = c(2004, 3))
test2 <- window(tsT_AV.imp, start = c(2004, 4))#Model 1 : Auto Exponential Smoothening Model
set.seed(301)
fit_auto_train_Var3 <- forecast(train2)
summary(fit_auto_train_Var3)##
## Forecast method: STL + ETS(A,N,N)
##
## Model Information:
## ETS(A,N,N)
##
## Call:
## ets(y = na.interp(x), model = etsmodel, allow.multiplicative.trend = allow.multiplicative.trend)
##
## Smoothing parameters:
## alpha = 0.9999
##
## Initial states:
## l = 21.3691
##
## sigma: 2.557
##
## AIC AICc BIC
## 20992.54 20992.55 21009.62
##
## Error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 0.002453102 2.55584 1.759238 -3.015496 13.56144 0.421226 0.0730533
##
## Forecasts:
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 2004.0082 18.06044 14.78350513 21.33738 13.0488004 23.07208
## 2004.0110 18.87994 14.24588158 23.51399 11.7927614 25.96711
## 2004.0137 18.71912 13.04368482 24.39456 10.0392885 27.39896
## 2004.0164 20.65887 14.10549253 27.21225 10.6363434 30.68140
## 2004.0192 17.99232 10.66545156 25.31918 6.7868443 29.19779
## 2004.0219 16.02033 7.99418310 24.04648 3.7453959 28.29527
## 2004.0247 20.11563 11.44641754 28.78484 6.8572138 33.37405
## 2004.0274 21.98155 12.71378748 31.24931 7.8077311 36.15537
## 2004.0301 21.76538 11.93545311 31.59532 6.7318017 36.79897
## 2004.0329 19.58277 9.22112606 29.94442 3.7360020 35.42954
## 2004.0356 18.75602 7.88863947 29.62339 2.1357980 35.37623
## 2004.0384 19.47598 8.12538457 30.82658 2.1167422 36.83522
## 2004.0411 20.18772 8.37365074 32.00178 2.1196615 38.25577
## 2004.0438 18.85494 6.59490960 31.11497 0.1048418 37.60504
## 2004.0466 19.79636 7.10602989 32.48669 0.3881747 39.20455
## 2004.0493 18.03219 4.92568342 31.13871 -2.0124847 38.07687
## 2004.0521 16.92514 3.41526164 30.43502 -3.7364357 37.58671
## 2004.0548 18.45992 4.55837292 32.36146 -2.8006605 39.72050
## 2004.0575 20.17406 5.89158206 34.45653 -1.6691039 42.01722
## 2004.0603 19.23714 4.58363750 33.89065 -3.1734605 41.64775
## 2004.0630 19.73808 4.72270773 34.75345 -3.2259506 42.70211
## 2004.0658 19.50550 4.13678384 34.87423 -3.9989255 43.00993
## 2004.0685 17.90914 2.19501780 33.62327 -6.1235377 41.94182
## 2004.0712 19.15798 3.10588300 35.21008 -5.3915851 43.70755
## 2004.0740 21.87553 5.49242964 38.25863 -3.1802609 46.93133
## 2004.0767 20.53740 3.82985132 37.24495 -5.0145910 46.08939
## 2004.0795 20.19807 3.17225357 37.22388 -5.8406682 46.23680
## 2004.0822 22.20058 4.86234514 39.53882 -4.3159639 48.71713
## 2004.0849 23.09218 5.44704563 40.73731 -3.8937228 50.07808
## 2004.0877 23.81598 5.86920433 41.76276 -3.6312459 51.26321
## 2004.0904 23.59367 5.35023262 41.83711 -4.3072594 51.49460
## 2004.0932 20.37457 1.83922321 38.90992 -7.9727975 48.72194
## 2004.0959 18.87838 0.05564178 37.70111 -9.9085114 47.66526
## 2004.0986 18.53407 -0.57172769 37.63986 -10.6857253 47.75386
## 2004.1014 19.23206 -0.15266143 38.61679 -10.4143156 48.87845
## 2004.1041 20.80432 1.14462373 40.46402 -9.2625923 50.87124
## 2004.1068 22.68452 2.75364049 42.61540 -7.7971293 53.16617
## 2004.1096 21.17052 0.97210517 41.36894 -9.7202913 52.06134
## 2004.1123 21.41336 0.95089793 41.87582 -9.8812736 52.70799
## 2004.1151 23.78461 3.06146980 44.50774 -7.9086960 55.47791
## 2004.1178 22.95430 1.97372046 43.93487 -9.1327253 55.04132
## 2004.1205 19.52718 -1.70771447 40.76207 -12.9487880 52.00315
## 2004.1233 20.44717 -1.03902995 41.93337 -12.4131380 53.30748
## 2004.1260 21.06967 -0.66493174 42.80428 -12.1705361 54.30988
## 2004.1288 20.29387 -1.68632462 42.27407 -13.3219393 53.90969
## 2004.1315 20.69749 -1.52559457 42.92057 -13.2897830 54.68476
## 2004.1342 19.67898 -2.78435740 42.14232 -14.6757294 54.03369
## 2004.1370 19.71554 -2.98551170 42.41659 -15.0027213 54.43380
## 2004.1397 21.06769 -1.86860871 44.00399 -14.0103517 56.14573
## 2004.1425 23.22396 0.05480506 46.39312 -12.2102071 58.65814
## 2004.1452 23.90914 0.50943289 47.30884 -11.8776217 59.69589
## 2004.1479 25.24340 1.61540284 48.87140 -10.8925034 61.37930
## 2004.1507 24.71145 0.85734647 48.56556 -11.7702549 61.19316
## 2004.1534 22.57550 -1.50259109 46.65360 -14.2487637 59.39977
## 2004.1562 22.35381 -1.94620413 46.65383 -14.8098550 59.51748
## 2004.1589 22.88516 -1.63476971 47.40509 -14.6148357 60.38515
## 2004.1616 22.18454 -2.55334340 46.92243 -15.6487896 60.01788
## 2004.1644 22.40008 -2.55386400 47.35402 -15.7636827 60.56384
## 2004.1671 25.00777 -0.16037294 50.17591 -13.4835823 63.49912
## 2004.1699 24.79341 -0.58712776 50.17394 -14.0227709 63.60958
## 2004.1726 24.51304 -1.07812323 50.10420 -14.6252670 63.65135
## 2004.1753 24.73004 -1.07003504 50.53011 -14.7277692 64.18785
## 2004.1781 23.01030 -2.99700294 49.01761 -16.7644392 62.78505
## 2004.1808 19.34047 -6.87243035 45.55337 -20.7487015 59.42964
## 2004.1836 19.77775 -6.63914646 46.19464 -20.6234054 60.17890
## 2004.1863 20.44623 -6.17309130 47.06556 -20.2645106 61.15698
## 2004.1890 22.58076 -4.23946736 49.40099 -18.4372381 63.59876
## 2004.1918 25.06703 -1.95260294 52.08667 -16.2559345 66.39000
## 2004.1945 24.72328 -2.49430822 51.94086 -16.9024272 66.34898
## 2004.1973 23.85013 -3.56397314 51.26423 -18.0761229 65.77638
## 2004.2000 23.35898 -4.25024774 50.96820 -18.8656878 65.58364
## 2004.2027 24.59989 -3.20308239 52.40287 -17.9210879 67.12087
## 2004.2055 26.31226 -1.68312878 54.30764 -16.5029900 69.12750
## 2004.2082 24.93436 -3.25211865 53.12084 -18.1731402 68.04186
## 2004.2110 23.10982 -5.26647174 51.48611 -20.2879724 66.50761
## 2004.2137 23.14327 -5.42156892 51.70811 -20.5428811 66.82942
## 2004.2164 24.91530 -3.83685172 53.66745 -19.0573208 68.88792
## 2004.2192 24.64446 -4.29378880 53.58271 -19.6127730 68.90170
## 2004.2219 24.37121 -4.75195240 53.49437 -20.1688222 68.91124
## 2004.2247 25.42344 -3.88346491 54.73034 -19.3976028 70.24448
## 2004.2274 25.97598 -3.51352130 55.46548 -19.1243212 71.07628
## 2004.2301 27.92252 -1.74845620 57.59350 -17.4553232 73.30037
## 2004.2329 27.16013 -2.69122227 57.01148 -18.4935724 72.81383
## 2004.2356 27.41139 -2.61925183 57.44203 -18.5165116 73.33929
## 2004.2384 28.75407 -1.45479698 58.96293 -17.4464031 74.95454
## 2004.2411 28.01375 -2.37228816 58.39980 -18.4576873 74.48520
## 2004.2438 27.64453 -2.91766587 58.20672 -19.0963142 74.38537
## 2004.2466 26.55936 -4.17797805 57.29670 -20.4493413 73.56806
## 2004.2493 28.07138 -2.84010822 58.98287 -19.2036610 75.34642
## 2004.2521 29.88792 -1.19673925 60.97258 -17.6519651 77.42781
## 2004.2548 29.35958 -1.89730001 60.61645 -18.4436911 77.16284
## 2004.2575 27.81721 -3.61094164 59.24535 -20.2479983 75.88241
## 2004.2603 27.63597 -3.96252545 59.23446 -20.6897564 75.96169
## 2004.2630 29.13788 -2.63003675 60.90581 -19.4469583 77.72273
## 2004.2658 29.67549 -2.26096474 61.61194 -19.1671012 78.51808
## 2004.2685 29.39689 -2.70720578 61.50099 -19.7020888 78.49587
## 2004.2712 28.35751 -3.91336623 60.62838 -20.9965348 77.71155
## 2004.2740 29.00005 -3.43674147 61.43684 -20.6077416 78.60784
## 2004.2767 27.59868 -5.00318529 60.20054 -22.2615700 77.45893
## 2004.2795 27.82218 -4.94392219 60.58829 -22.2892513 77.93362
## 2004.2822 29.22809 -3.70143756 62.15762 -21.1332774 79.58946
## 2004.2849 30.13013 -2.96201400 63.22228 -20.4799374 80.74020
## 2004.2877 30.72087 -2.53309942 63.97483 -20.1366854 81.57842
## 2004.2904 30.04487 -3.37013474 63.45987 -21.0589684 81.14870
## 2004.2932 30.32132 -3.25394537 63.89659 -21.0276179 81.67026
## 2004.2959 30.57247 -3.16230125 64.30724 -21.0204096 82.16535
## 2004.2986 30.29348 -3.60003826 64.18701 -21.5421850 82.12915
## 2004.3014 29.67076 -4.38077309 63.72230 -22.4065665 81.74809
## 2004.3041 29.88011 -4.32870630 64.08893 -22.4377601 82.19798
## 2004.3068 31.41306 -2.95232192 65.77844 -21.1442549 83.97037
## 2004.3096 31.96973 -2.55150346 66.49096 -20.8259398 84.76540
## 2004.3123 31.43152 -3.24486270 66.10791 -21.6014316 84.46447
## 2004.3151 31.07754 -3.75330835 65.90838 -22.1916440 84.34672
## 2004.3178 30.93141 -4.05321003 65.91604 -22.5729514 84.43578
## 2004.3205 31.02438 -4.11335486 66.16211 -22.7141457 84.76290
## 2004.3233 31.56732 -3.72284781 66.85750 -22.4043364 85.53898
## 2004.3260 31.30766 -4.13429777 66.74962 -22.8961371 85.51146
## 2004.3288 29.25900 -6.33409444 64.85210 -25.1759418 83.69395
## 2004.3315 29.20720 -6.53639461 64.95080 -25.4579118 83.87232
## 2004.3342 30.20564 -5.68783009 66.09910 -24.6886830 85.09995
## 2004.3370 32.03071 -4.01199693 68.07343 -23.0918557 87.15328
## 2004.3397 30.49587 -5.69547118 66.68721 -24.8540099 85.84575
## 2004.3425 30.30228 -6.03708256 66.64164 -25.2739795 85.87854
## 2004.3452 29.46330 -7.02348810 65.95008 -26.3384254 85.26502
## 2004.3479 30.11734 -6.51627229 66.75095 -25.9089359 86.14362
## 2004.3507 31.44472 -5.33513969 68.22457 -24.8052193 87.69465
## 2004.3534 30.93522 -5.99030403 67.86073 -25.5374931 87.40792
## 2004.3562 31.74299 -5.32762224 68.81360 -24.9516177 88.43759
## 2004.3589 32.45148 -4.76365521 69.66661 -24.4641576 89.36712
## 2004.3616 32.15963 -5.19946973 69.51873 -24.9761832 89.29545
## 2004.3644 31.91213 -5.59038808 69.41464 -25.4430200 89.26727
## 2004.3671 32.14132 -5.50406145 69.78670 -25.4323226 89.71496
## 2004.3699 32.35224 -5.43546504 70.13995 -25.4390695 90.14356
## 2004.3726 32.18983 -5.73966716 70.11933 -25.8183322 90.19800
## 2004.3753 32.69823 -5.37253481 70.76900 -25.5259808 90.92244
## 2004.3781 32.14524 -6.06626436 70.35675 -26.2942149 90.58470
## 2004.3808 33.10437 -5.24736595 71.45610 -25.5495477 91.75828
## 2004.3836 33.69082 -4.80062765 72.18227 -25.1767701 92.55841
## 2004.3863 33.61506 -5.01559678 72.24572 -25.4654325 92.69556
## 2004.3890 32.89056 -5.87881214 71.65993 -26.4020765 92.18319
## 2004.3918 31.33293 -7.57465080 70.24052 -28.1710820 90.83695
## 2004.3945 31.81424 -7.23107430 70.85955 -27.9004133 91.52889
## 2004.3973 31.79357 -7.38897831 70.97613 -28.1309689 91.71812
## 2004.4000 32.67250 -6.64681294 71.99182 -27.4612015 92.80621
## 2004.4027 32.57865 -6.87695239 72.03426 -27.7634880 92.92079
## 2004.4055 33.75419 -5.83723784 73.34561 -26.7956722 94.30405
## 2004.4082 34.36927 -5.35750639 74.09605 -26.3875936 95.12614
## 2004.4110 34.47923 -5.38244464 74.34091 -26.4839414 95.44240
## 2004.4137 34.61665 -5.37946379 74.61277 -26.5521293 95.78544
## 2004.4164 34.80720 -5.32290644 74.93731 -26.5665022 96.18090
## 2004.4192 33.55523 -6.70842054 73.81888 -28.0227106 95.13317
## 2004.4219 33.99493 -6.40182831 74.39168 -27.7865789 95.77643
## 2004.4247 32.81941 -7.71001367 73.34883 -29.1649935 94.80381
## 2004.4274 32.51460 -8.14705303 73.17626 -29.6720329 94.70124
## 2004.4301 32.94550 -7.84795495 73.73896 -29.4427079 95.33372
## 2004.4329 33.28041 -7.64442993 74.20525 -29.3087313 95.86955
## 2004.4356 33.92599 -7.12980744 74.98179 -28.8634346 96.71542
## 2004.4384 33.27267 -7.91367296 74.45901 -29.7164056 96.26174
## 2004.4411 33.49552 -7.82094826 74.81200 -29.6925680 96.68362
## 2004.4438 33.17568 -8.27051588 74.62187 -30.2108064 96.56217
## 2004.4466 32.94135 -8.63416582 74.51686 -30.6429128 96.52561
## 2004.4493 33.06158 -8.64284539 74.76601 -30.7198367 96.84300
## 2004.4521 33.92229 -7.91065445 75.75524 -30.0556797 97.90027
## 2004.4548 32.91469 -9.04637986 74.87577 -31.2592307 97.08862
## 2004.4575 32.56952 -9.51928668 74.65833 -31.7997566 96.93880
## 2004.4603 33.65607 -8.56009244 75.87222 -30.9079768 98.22011
## 2004.4630 33.67842 -8.66470004 76.02155 -31.0797962 98.43665
## 2004.4658 33.45668 -9.01303313 75.92639 -31.4951401 98.40850
## 2004.4685 34.09710 -8.49882616 76.69302 -31.0477448 99.24194
## 2004.4712 34.21924 -8.50251875 76.94100 -31.1180517 99.55653
## 2004.4740 34.35679 -8.49043921 77.20401 -31.1723908 99.88597
## 2004.4767 34.02227 -8.95005589 76.99460 -31.6982322 99.74278
## 2004.4795 34.53089 -8.56617492 77.62796 -31.3803838 100.44217
## 2004.4822 34.78040 -8.44104898 78.00184 -31.3210998 100.88189
## 2004.4849 34.53557 -8.80989633 77.88104 -31.7556001 100.82674
## 2004.4877 34.28228 -9.18685478 77.75141 -32.1980243 100.76258
## 2004.4904 34.52241 -9.07004511 78.11486 -32.1464946 101.19131
## 2004.4932 35.11934 -8.59607915 78.83476 -31.7376244 101.97631
## 2004.4959 35.21505 -8.62299271 79.05309 -31.8294512 102.25955
## 2004.4986 34.52594 -9.43438535 78.48627 -32.7055760 101.75746
## 2004.5014 34.36932 -9.71294538 78.45159 -33.0486886 101.78733
## 2004.5041 34.58571 -9.61816856 78.78958 -33.0182863 102.18970
## 2004.5068 34.33396 -9.99118674 78.65911 -33.4555024 102.12342
## 2004.5096 34.22226 -10.22382831 78.66835 -33.7521667 102.19669
## 2004.5123 34.56059 -10.00610961 79.12730 -33.5982970 102.71948
## 2004.5151 34.66400 -10.02298746 79.35099 -33.6788515 103.00686
## 2004.5178 34.70945 -10.09751084 79.51640 -33.8168806 103.23577
## 2004.5205 34.44202 -10.48458591 79.36862 -34.2672919 103.15132
## 2004.5233 34.73400 -10.31192374 79.77993 -34.1577976 103.62581
## 2004.5260 34.52637 -10.63856735 79.69131 -34.5474422 103.60019
## 2004.5288 34.51031 -10.77332778 79.79395 -34.7450381 103.76566
## 2004.5315 34.17055 -11.23148030 79.57257 -35.2658618 103.60696
## 2004.5342 33.86918 -11.65092632 79.38929 -35.7478160 103.48618
## 2004.5370 34.45938 -11.17850676 80.09726 -35.3377429 104.25650
## 2004.5397 35.04309 -10.71226325 80.79845 -34.9336854 105.01987
## 2004.5425 34.65573 -11.21679868 80.52826 -35.5002476 104.81170
## 2004.5452 33.70113 -12.28826497 79.69053 -36.6335825 104.03585
## 2004.5479 34.08637 -12.01960559 80.19235 -36.4266350 104.59938
## 2004.5507 33.22014 -13.00212194 79.44240 -37.4707076 103.91098
## 2004.5534 33.36215 -12.97609681 79.70040 -37.5060842 104.23039
## 2004.5562 33.56557 -12.88838177 80.01952 -37.4796176 104.61075
## 2004.5589 34.24965 -12.31971869 80.81901 -36.9720508 105.47134
## 2004.5616 34.49290 -12.19159533 81.17739 -36.9048727 105.89067
## 2004.5644 33.86433 -12.93500589 80.66367 -37.7090786 105.43774
## 2004.5671 34.21427 -12.69963567 81.12817 -37.5343548 105.96289
## 2004.5699 34.51754 -12.51064646 81.54573 -37.4058643 106.44094
## 2004.5726 34.45110 -12.69109025 81.59330 -37.6466602 106.54887
## 2004.5753 34.71092 -12.54500652 81.96685 -37.5607829 106.98262
## 2004.5781 34.52445 -12.84493428 81.89384 -37.9207726 106.96968
## 2004.5808 33.84145 -13.64112900 81.32402 -38.7768857 106.45978
## 2004.5836 33.84735 -13.74814483 81.44284 -38.9436775 106.63838
## 2004.5863 34.15946 -13.54868283 81.86761 -38.8038499 107.12278
## 2004.5890 34.48478 -13.33575285 82.30531 -38.6504139 107.61997
## 2004.5918 34.37644 -13.55622103 82.30909 -38.9302365 107.68311
## 2004.5945 34.42376 -13.62075525 82.46828 -39.0539866 107.90151
## 2004.5973 34.22886 -13.92726106 82.38498 -39.4195708 107.87729
## 2004.6000 34.14968 -14.11778102 82.41715 -39.6690326 107.96840
## 2004.6027 33.55321 -14.82534495 81.93176 -40.4354026 107.54181
## 2004.6055 33.01051 -15.47887038 81.49990 -41.1475995 107.16863
## 2004.6082 32.69943 -15.90053249 81.29939 -41.6277992 107.02666
## 2004.6110 32.50444 -16.20585484 81.21473 -41.9915262 107.00040
## 2004.6137 33.27646 -15.54391130 82.09683 -41.3878554 107.94078
## 2004.6164 33.05548 -15.87472155 81.98569 -41.7768073 107.88777
## 2004.6192 32.47215 -16.56764302 81.51194 -42.5277402 107.47204
## 2004.6219 31.68214 -17.46698946 80.83128 -43.4849687 106.84926
## 2004.6247 31.49242 -17.76581148 80.75065 -43.8415443 106.82638
## 2004.6274 32.16547 -17.20161578 81.53256 -43.3349745 107.66592
## 2004.6301 32.45148 -17.02422549 81.92719 -43.2150834 108.11805
## 2004.6329 32.14579 -17.43829611 81.72988 -43.6865272 107.97811
## 2004.6356 32.77993 -16.91230318 82.47216 -43.2177824 108.77764
## 2004.6384 32.81377 -16.98637695 82.61391 -43.3489799 108.97651
## 2004.6411 33.25643 -16.65138908 83.16425 -43.0709922 109.58385
## 2004.6438 33.41547 -16.59979407 83.43073 -43.0762748 109.90721
## 2004.6466 32.65538 -17.46709931 82.77785 -44.0003356 109.31109
## 2004.6493 32.34972 -17.87973996 82.57918 -44.4696107 109.16905
## 2004.6521 32.17493 -18.16128959 82.51115 -44.8076744 109.15753
## 2004.6548 31.62662 -18.81613016 82.06937 -45.5189095 108.77215
## 2004.6575 31.31377 -19.23528501 81.86283 -45.9943400 108.62189
## 2004.6603 31.70802 -18.94712183 82.36316 -45.7623343 109.17837
## 2004.6630 31.14760 -19.61340297 81.90861 -46.4846556 108.77986
## 2004.6658 30.99661 -19.87003576 81.86326 -46.7972119 108.79043
## 2004.6685 31.20398 -19.76808770 82.17605 -46.7510715 109.15904
## 2004.6712 31.44393 -19.63334421 82.52121 -46.6720205 109.55988
## 2004.6740 30.55986 -20.62240918 81.74212 -47.7166634 108.83637
## 2004.6767 29.84914 -21.43790029 81.13618 -48.5876187 108.28590
## 2004.6795 30.51220 -20.87939984 81.90380 -48.0844694 109.10887
## 2004.6822 30.88390 -20.61205139 82.37984 -47.8723597 109.64015
## 2004.6849 30.75301 -20.84707512 82.35310 -48.1625104 109.66853
## 2004.6877 29.30193 -22.40208682 81.00594 -49.7725381 108.37639
## 2004.6904 29.30359 -22.50414016 81.11132 -49.9294971 108.53668
## 2004.6932 28.93462 -22.97662306 80.84587 -50.4567759 108.32602
## 2004.6959 28.63842 -23.37613030 80.65297 -50.9109700 108.18781
## 2004.6986 27.24644 -24.87121248 79.36409 -52.4606307 106.95351
## 2004.7014 27.21761 -25.00294077 79.43816 -52.6468297 107.08205
## 2004.7041 28.01493 -24.30831848 80.33817 -52.0065710 108.03642
## 2004.7068 28.33581 -24.08992473 80.76155 -51.8424344 108.51406
## 2004.7096 28.25290 -24.27513601 80.78093 -52.0817969 108.58759
## 2004.7123 27.58470 -25.04542811 80.21483 -52.9061350 108.07554
## 2004.7151 27.67943 -25.05259146 80.41146 -52.9672397 108.32611
## 2004.7178 29.08095 -23.75277957 81.91467 -51.7212652 109.88316
## 2004.7205 29.79034 -23.14488842 82.72558 -51.1671079 110.74780
## 2004.7233 29.90540 -23.13114288 82.94195 -51.2069934 111.01780
## 2004.7260 29.60713 -23.53053396 82.74479 -51.6599133 110.87417
## 2004.7288 26.43609 -26.80249465 79.67468 -54.9853011 107.85749
## 2004.7315 25.38571 -27.95361512 78.72503 -56.1897476 106.96117
## 2004.7342 26.23353 -27.20633615 79.67340 -55.4956942 107.96276
## 2004.7370 25.96302 -27.57721005 79.50324 -55.9196936 107.84573
## 2004.7397 27.14875 -26.49164405 80.78915 -54.8871538 109.18466
## 2004.7425 27.30707 -26.43330439 81.04745 -54.8817415 109.49589
## 2004.7452 28.03361 -25.80655882 81.87379 -54.3078249 110.37505
## 2004.7479 26.86605 -27.07373376 80.80584 -55.6277312 109.35983
## 2004.7507 27.11628 -26.92293781 81.15549 -55.5295693 109.76212
## 2004.7534 27.69460 -26.44385839 81.83306 -55.1030274 110.49223
## 2004.7562 26.46162 -27.77589991 80.69915 -56.4875102 109.41076
## 2004.7589 24.06916 -30.26724245 78.40557 -59.0311984 107.16953
## 2004.7616 23.34782 -31.08728819 77.78293 -59.9034948 106.59914
## 2004.7644 24.40858 -30.12505282 78.94222 -58.9934154 107.81058
## 2004.7671 25.29966 -29.33232365 79.93164 -58.2527482 108.85207
## 2004.7699 26.80589 -27.92426309 81.53604 -56.8966561 110.50844
## 2004.7726 28.42633 -26.40182019 83.25448 -55.4260886 112.27874
## 2004.7753 28.45967 -26.46630131 83.38564 -55.5423525 112.46169
## 2004.7781 27.98128 -27.04233826 83.00489 -56.1700802 112.13263
## 2004.7808 26.41156 -28.70952601 81.53265 -57.8888672 110.71199
## 2004.7836 26.16925 -29.04913402 81.38764 -58.2799833 110.61849
## 2004.7863 26.11669 -29.19883364 81.43220 -58.4811004 110.71447
## 2004.7890 24.65721 -30.75526519 80.06969 -60.0888593 109.40329
## 2004.7918 24.14158 -31.36768819 79.65085 -60.7525201 109.03568
## 2004.7945 24.02966 -31.57623340 79.63555 -61.0122138 109.07153
## 2004.7973 24.26027 -31.44207515 79.96261 -60.9291154 109.44965
## 2004.8000 26.01220 -29.78642802 81.81084 -59.3244398 111.34885
## 2004.8027 27.12352 -28.77123718 83.01827 -58.3601327 112.60717
## 2004.8055 26.30034 -29.69037402 82.29105 -59.3300659 111.93074
## 2004.8082 25.94620 -30.14030095 82.03271 -59.8307023 111.72311
## 2004.8110 25.15128 -31.03085535 81.33341 -60.7718798 111.07443
## 2004.8137 25.16164 -31.11595530 81.43924 -60.9075167 111.23080
## 2004.8164 24.55142 -31.82148425 80.92432 -61.6634971 110.76634
## 2004.8192 24.17858 -32.28946884 80.64663 -62.1818479 110.53901
## 2004.8219 21.91674 -34.64629400 78.47977 -64.5889546 108.42243
## 2004.8247 22.38637 -34.27148807 79.04423 -64.2643460 109.03708
## 2004.8274 23.31825 -33.43427049 80.07078 -63.4772418 110.11375
## 2004.8301 24.54557 -32.30146265 81.39260 -62.3944639 111.48560
## 2004.8329 21.92996 -35.01142329 78.87135 -65.1543714 109.01429
## 2004.8356 19.74903 -37.28654903 76.78461 -67.4793614 106.97742
## 2004.8384 22.37106 -34.75855665 79.50068 -65.0011511 109.74328
## 2004.8411 24.90459 -32.31891937 82.12809 -62.6112140 112.42039
## 2004.8438 22.39975 -34.91748894 79.71699 -65.2594024 110.05890
## 2004.8466 19.78895 -37.62187191 77.19976 -68.0133232 107.59122
## 2004.8493 20.16906 -37.33518426 77.67331 -67.7760928 108.11421
## 2004.8521 19.88838 -37.70913902 77.48590 -68.1994245 107.97619
## 2004.8548 20.54781 -37.14283842 78.23845 -67.6824210 108.77803
## 2004.8575 22.08421 -35.69941312 79.86783 -66.2882135 110.45663
## 2004.8603 24.79758 -33.07886568 82.67402 -63.7168046 113.31196
## 2004.8630 21.58510 -36.38402335 79.55422 -67.0710223 110.24122
## 2004.8658 19.51064 -38.55100972 77.57229 -69.2869903 108.30827
## 2004.8685 20.23679 -37.91723603 78.39083 -68.7021203 109.17571
## 2004.8712 19.88132 -38.36494411 78.12759 -69.1986545 108.96130
## 2004.8740 20.64938 -37.68896956 78.98774 -68.5714289 109.87020
## 2004.8767 19.93514 -38.49515820 78.36544 -69.4262897 109.29657
## 2004.8795 18.69222 -39.82987482 77.21432 -70.8096019 108.19405
## 2004.8822 19.87604 -38.73770907 78.48980 -69.7659557 109.51804
## 2004.8849 20.17560 -38.52966452 78.88087 -69.6063550 109.95756
## 2004.8877 20.09857 -38.69806847 78.89520 -69.8231273 110.02026
## 2004.8904 20.45215 -38.43571719 79.34001 -69.6090694 110.51336
## 2004.8932 21.63795 -37.34099768 80.61690 -68.5625685 111.83848
## 2004.8959 20.38060 -38.68929700 79.45050 -69.9590121 110.72021
## 2004.8986 19.90285 -39.25785926 79.06355 -70.5756446 110.38134
## 2004.9014 20.07142 -39.17995157 79.32279 -70.5457336 110.68858
## 2004.9041 19.48117 -39.86073548 78.82307 -71.2744407 110.23677
## 2004.9068 19.36476 -40.06753627 78.79705 -71.5290918 110.25861
## 2004.9096 21.76021 -37.76233736 81.28276 -69.2716705 112.79209
## 2004.9123 22.12976 -37.48290676 81.74242 -69.0399452 113.29946
## 2004.9151 18.56448 -41.13816826 78.26712 -72.7428399 109.87180
## 2004.9178 17.62145 -42.17103940 77.41394 -73.8232727 109.06618
## 2004.9205 18.14078 -41.74142648 78.02298 -73.4411500 109.72270
## 2004.9233 20.93677 -39.03501158 80.90855 -70.7821542 112.65569
## 2004.9260 18.99173 -41.06949386 79.05295 -72.8639850 110.84744
## 2004.9288 19.15340 -40.99713113 79.30394 -72.8389003 111.14571
## 2004.9315 16.36170 -43.87801636 76.60141 -75.7669935 108.49038
## 2004.9342 16.44368 -43.88507521 76.77244 -75.8211905 108.70856
## 2004.9370 17.20845 -43.20922285 77.62612 -75.1924069 109.60931
## 2004.9397 19.26835 -41.23811064 79.77480 -73.2682942 111.80499
## 2004.9425 19.16184 -41.43326716 79.75696 -73.5103814 111.83407
## 2004.9452 17.72538 -42.95825225 78.40902 -75.0822286 110.53300
## 2004.9479 18.03385 -42.73817743 78.80589 -74.9089476 110.97666
## 2004.9507 16.50794 -44.35235612 77.36824 -76.5698522 109.58574
## 2004.9534 16.33963 -44.60880873 77.28807 -76.8729630 109.55222
## 2004.9562 17.17020 -43.86625109 78.20665 -76.1769962 110.51739
## 2004.9589 16.35632 -44.76801605 77.48066 -77.1252849 109.83792
## 2004.9616 15.77002 -45.44207084 76.98212 -77.8457966 109.38585
## 2004.9644 15.32870 -45.97103216 76.62843 -78.4211484 109.07854
## 2004.9671 13.77887 -47.60836380 75.16611 -80.1048042 107.66255
## 2004.9699 14.25122 -47.22340486 75.72584 -79.7661036 108.26854
## 2004.9726 14.38582 -47.17605935 75.94770 -79.7649507 108.53659
## 2004.9753 15.38716 -46.26185866 77.03618 -78.8968772 109.67120
## 2004.9781 17.05263 -44.68340100 78.78866 -77.3644817 111.46974
## 2004.9808 18.41813 -43.40479135 80.24105 -76.1318693 112.96813
## 2004.9836 19.54626 -42.36343083 81.45595 -75.1364416 114.22896
## 2004.9863 15.81055 -46.18579092 77.80689 -79.0046701 110.62577
## 2004.9890 16.28706 -45.79580064 78.36993 -78.6604843 111.23461
## 2004.9918 17.03439 -45.13488541 79.20366 -78.0453097 112.11408
## 2004.9945 18.75844 -43.49711501 81.01400 -76.4532165 113.97010
## 2004.9973 20.30549 -42.03623758 82.64721 -75.0379531 115.64893
## 2005.0000 20.01323 -42.41454135 82.44100 -75.4618078 115.48827
## 2005.0027 20.16132 -42.35237980 82.67502 -75.4451346 115.76778
## 2005.0055 18.79990 -43.79960966 81.39942 -76.9377903 114.53760
## 2005.0082 18.06044 -44.62476717 80.74565 -77.8083116 113.92919
## 2005.0110 18.87994 -43.89084857 81.65072 -77.1196947 114.87957
## 2005.0137 18.71912 -44.13712056 81.57537 -77.4112068 114.84946
## 2005.0164 20.65887 -42.28271843 83.60046 -75.6019833 116.91973
## 2005.0192 17.99232 -45.03450358 81.01913 -78.3988860 114.38352
## 2005.0219 16.02033 -47.09159934 79.13227 -80.5010383 112.54170
## 2005.0247 20.11563 -43.08130195 83.31256 -76.5357368 116.76700
## 2005.0274 21.98155 -41.30026815 85.26337 -74.7996384 118.76274
## 2005.0301 21.76538 -41.60120354 85.13197 -75.1454490 118.67622
## 2005.0329 19.58277 -43.86847412 83.03402 -77.4575349 116.62308
## 2005.0356 18.75602 -44.77977587 82.29181 -78.4135922 115.92562
## 2005.0384 19.47598 -44.14424426 83.09620 -77.8227567 116.77472
## 2005.0411 20.18772 -43.51682783 83.89226 -77.2399771 117.61541
## 2005.0438 18.85494 -44.93381556 82.64369 -78.7015427 116.41142
## 2005.0466 19.79636 -44.07649318 83.66921 -77.8887394 117.48146
## 2005.0493 18.03219 -45.92464660 81.98904 -79.7813534 115.84574
## 2005.0521 16.92514 -47.11557984 80.96586 -81.0166888 114.86697
## 2005.0548 18.45992 -45.66456943 82.58441 -79.6100226 116.52986
## 2005.0575 20.17406 -44.03408851 84.38220 -78.0238280 118.37194
## 2005.0603 19.23714 -45.05455170 83.52884 -79.0885198 117.56281
## 2005.0630 19.73808 -44.63705708 84.11322 -78.7151965 118.19136
## 2005.0658 19.50550 -44.95296657 83.96398 -79.0752201 118.08623
## 2005.0685 17.90914 -46.63255399 82.45084 -80.7988646 116.61715
## 2005.0712 19.15798 -45.46683358 83.78280 -79.6771446 117.99311
## 2005.0740 21.87553 -42.83229568 86.58336 -77.0865506 120.83761
## 2005.0767 20.53740 -44.25333280 85.32813 -78.5514753 119.62628
## 2005.0795 20.19807 -44.67546500 85.07160 -79.0174390 119.41358
## 2005.0822 22.20058 -42.75564350 87.15681 -77.1413931 121.54256
## 2005.0849 23.09218 -41.94663885 88.13099 -76.3761084 122.56046
## 2005.0877 23.81598 -41.30531840 88.93728 -75.7784525 123.41042
## 2005.0904 23.59367 -41.61001090 88.79735 -76.1267542 123.31409
## 2005.0932 20.37457 -44.91138459 85.66053 -79.4716822 120.22083
## 2005.0959 18.87838 -46.48975329 84.24650 -81.0935503 118.85030
## 2005.0986 18.53407 -46.91612916 83.98427 -81.5633710 118.63151
## 2005.1014 19.23206 -46.30009946 84.76423 -80.9907317 119.45486
## 2005.1041 20.80432 -44.80970551 86.41835 -79.5436739 121.15232
## 2005.1068 22.68452 -43.01127120 88.38031 -77.7885218 123.15756
## 2005.1096 21.17052 -44.60692779 86.94797 -79.4274068 121.76845
## 2005.1123 21.41336 -44.44565274 87.27237 -79.3093066 122.13602
## 2005.1151 23.78461 -42.15586168 89.72507 -77.0626369 124.63185
## 2005.1178 22.95430 -43.06752992 88.97612 -78.0173733 123.92597
## 2005.1205 19.52718 -46.57590442 85.63026 -81.5687630 120.62312
## 2005.1233 20.44717 -45.73706968 86.63141 -80.7728906 121.66723
## 2005.1260 21.06967 -45.19562744 87.33497 -80.2743582 122.41370
## 2005.1288 20.29387 -46.05238432 86.64013 -81.1739724 121.76172
## 2005.1315 20.69749 -45.72963360 87.12461 -80.8940268 122.28900
## 2005.1342 19.67898 -46.82890340 86.18686 -82.0360496 121.39401
## 2005.1370 19.71554 -46.87300933 86.30408 -82.1228567 121.55393
## 2005.1397 21.06769 -45.60142389 87.73680 -80.8939208 123.02930
## 2005.1425 23.22396 -43.52561892 89.97355 -78.8607139 125.30864
## 2005.1452 23.90914 -42.92082019 90.73909 -78.2984620 126.11673
## 2005.1479 25.24340 -41.66683215 92.15363 -77.0869696 127.57377
## 2005.1507 24.71145 -42.27895902 91.70187 -77.7415412 127.16445
## 2005.1534 22.57550 -44.49499444 89.64600 -79.9999706 125.15097
## 2005.1562 22.35381 -44.79667436 89.50430 -80.3439940 125.05162
## 2005.1589 22.88516 -44.34522010 90.11554 -79.9348328 125.70515
## 2005.1616 22.18454 -45.12563403 89.49472 -80.7574896 125.12658
## 2005.1644 22.40008 -44.98980403 89.78996 -80.6638524 125.46401
## 2005.1671 25.00777 -42.46172287 92.47726 -78.1779142 128.19345
## 2005.1699 24.79341 -42.75560144 92.34241 -78.5138861 128.10070
## 2005.1726 24.51304 -43.11538986 92.14147 -78.9157184 127.94180
## 2005.1753 24.73004 -42.97772095 92.43780 -78.8200440 128.28012
## 2005.1781 23.01030 -44.77669336 90.79730 -80.6609618 126.68157
## 2005.1808 19.34047 -48.52567105 87.20661 -84.4518358 123.13278
## 2005.1836 19.77775 -48.16744526 87.72294 -84.1354577 123.69095
## 2005.1863 20.44623 -47.57791958 88.47039 -83.5877309 124.48020
## 2005.1890 22.58076 -45.52226140 90.68378 -81.5738233 126.73534
## 2005.1918 25.06703 -43.11476528 93.24883 -79.2080293 129.34210
## 2005.1945 24.72328 -43.53720887 92.98376 -79.6721270 129.11868
## 2005.1973 23.85013 -44.48895078 92.18921 -80.6654750 128.36574
## 2005.2000 23.35898 -45.05861083 91.77656 -81.2766934 127.99464
## 2005.2027 24.59989 -43.89611028 93.09589 -80.1557036 129.35549
## 2005.2055 26.31226 -42.26207267 94.88658 -78.5631292 131.18764
## 2005.2082 24.93436 -43.71820260 93.58693 -80.0606750 129.92940
## 2005.2110 23.10982 -45.62089358 91.84053 -82.0047348 128.22437
## 2005.2137 23.14327 -45.66550113 91.95204 -82.0906641 128.37720
## 2005.2164 24.91530 -43.97144226 93.80204 -80.4378802 130.26848
## 2005.2192 24.64446 -44.32016194 93.60908 -80.8278282 130.11675
## 2005.2219 24.37121 -44.67120945 93.41363 -81.2200575 129.96247
## 2005.2247 25.42344 -43.69668496 94.54356 -80.2866685 131.13355
## 2005.2274 25.97598 -43.22176196 95.17373 -79.8528347 131.80480
## 2005.2301 27.92252 -41.35275421 97.19780 -78.0248702 133.86991
## 2005.2329 27.16013 -42.19259417 96.51285 -78.9057074 133.22596
## 2005.2356 27.41139 -42.01869457 96.84147 -78.7727595 133.59553
## 2005.2384 28.75407 -40.75328851 98.26142 -77.5482594 135.05639
## 2005.2411 28.01375 -41.57078801 97.59830 -78.4066195 134.43413
## 2005.2438 27.64453 -42.01711566 97.30617 -78.8937625 134.18282
## 2005.2466 26.55936 -43.17930203 96.29802 -80.0967190 133.21544
## 2005.2493 28.07138 -41.74421375 97.88697 -78.7023560 134.84511
## 2005.2521 29.88792 -40.00451731 99.78036 -77.0033399 136.77918
## 2005.2548 29.35958 -40.60962563 99.32878 -77.6490840 136.36824
## 2005.2575 27.81721 -42.22867437 97.86309 -79.3087239 134.94314
## 2005.2603 27.63597 -42.48650975 97.75844 -79.6071061 134.87904
## 2005.2630 29.13788 -41.06110244 99.33687 -78.2222013 136.49797
## 2005.2658 29.67549 -40.59992736 99.95090 -77.8014847 137.15246
## 2005.2685 29.39689 -40.95486700 99.74865 -78.1968388 136.99062
## 2005.2712 28.35751 -42.07051420 98.78553 -79.3528567 136.06787
## 2005.2740 29.00005 -41.50415117 99.50425 -78.8268207 136.82692
## 2005.2767 27.59868 -42.98161888 98.17898 -80.3445719 135.54193
## 2005.2795 27.82218 -42.83412932 98.47850 -80.2373225 135.88169
## 2005.2822 29.22809 -41.50415572 99.96034 -78.9475458 137.40373
## 2005.2849 30.13013 -40.67796880 100.93823 -78.1615126 138.42177
## 2005.2877 30.72087 -40.16300489 101.60474 -77.6866595 139.12839
## 2005.2904 30.04487 -40.91469362 101.00443 -78.4784162 138.56815
## 2005.2932 30.32132 -40.71384937 101.35649 -78.3175972 138.96024
## 2005.2959 30.57247 -40.53823135 101.68317 -78.1819619 139.32690
## 2005.2986 30.29348 -40.89266493 101.47963 -78.5763358 139.16330
## 2005.3014 29.67076 -41.59075657 100.93228 -79.3143254 138.65585
## 2005.3041 29.88011 -41.45669681 101.21692 -79.2201215 138.98034
## 2005.3068 31.41306 -39.99895993 102.82508 -77.8021985 140.62831
## 2005.3096 31.96973 -39.51741988 103.45688 -77.3604304 141.29989
## 2005.3123 31.43152 -40.13067913 102.99372 -78.0134198 140.87646
## 2005.3151 31.07754 -40.55963727 102.71471 -78.4820665 140.63714
## 2005.3178 30.93141 -40.78065500 102.64348 -78.7427313 140.60556
## 2005.3205 31.02438 -40.76251075 102.81126 -78.7641928 140.81294
## 2005.3233 31.56732 -40.29430098 103.42895 -78.3355475 141.47020
## 2005.3260 31.30766 -40.62862623 103.24395 -78.7093961 141.32472
## 2005.3288 29.25900 -42.75186807 101.26987 -80.8721203 139.39013
## 2005.3315 29.20720 -42.87817531 101.29258 -81.0378691 139.45227
## 2005.3342 30.20564 -41.95417196 102.36544 -80.1532666 140.56454
## 2005.3370 32.03071 -40.20344644 104.26487 -78.4419012 142.50333
## 2005.3397 30.49587 -41.81256733 102.80431 -80.0903419 141.08208
## 2005.3425 30.30228 -42.08035703 102.68492 -80.3974110 141.00197
## 2005.3452 29.46330 -42.99346541 101.92006 -81.3497585 140.27635
## 2005.3479 30.11734 -42.41346993 102.64815 -80.8089621 141.04364
## 2005.3507 31.44472 -41.16006829 104.04950 -79.5947196 142.48415
## 2005.3534 30.93522 -41.74346748 103.61390 -80.2172380 142.08767
## 2005.3562 31.74299 -41.00951784 104.49549 -79.5223678 143.00834
## 2005.3589 32.45148 -40.37477379 105.27773 -78.9266637 143.82962
## 2005.3616 32.15963 -40.74029578 105.05956 -79.3311860 143.65045
## 2005.3644 31.91213 -41.06139987 104.88565 -79.6912512 143.51550
## 2005.3671 32.14132 -40.90573117 105.18837 -79.5745042 143.85714
## 2005.3699 32.35224 -40.76825891 105.47275 -79.4759146 144.18040
## 2005.3726 32.18983 -41.00404553 105.38371 -79.7505448 144.13021
## 2005.3753 32.69823 -40.56895228 105.96541 -79.3542562 144.75072
## 2005.3781 32.14524 -41.19516992 105.48566 -80.0192398 144.30973
## 2005.3808 33.10437 -40.30920304 106.51794 -79.1720002 145.38074
## 2005.3836 33.69082 -39.79583427 107.17748 -78.6973201 146.07896
## 2005.3863 33.61506 -39.94460564 107.17473 -78.8847417 146.11487
## 2005.3890 32.89056 -40.74205069 106.52316 -79.7207987 145.50191
## 2005.3918 31.33293 -42.37254138 105.03841 -81.3898631 144.05573
## 2005.3945 31.81424 -41.96403420 105.59251 -81.0198915 144.64836
## 2005.3973 31.79357 -42.05741988 105.64457 -81.1517749 144.73892
## 2005.4000 32.67250 -41.25114367 106.59615 -80.3839584 145.72896
## 2005.4027 32.57865 -41.41757500 106.57488 -80.5888117 145.74612
## 2005.4055 33.75419 -40.31455036 107.82292 -79.5241715 147.03255
## 2005.4082 34.36927 -39.77190226 108.51045 -79.0198702 147.75842
## 2005.4110 34.47923 -39.73431275 108.69278 -79.0205900 147.97905
## 2005.4137 34.61665 -39.66918862 108.90250 -78.9937380 148.22704
## 2005.4164 34.80720 -39.55086809 109.16527 -78.9136523 148.52805
## 2005.4192 33.55523 -40.87499481 107.98546 -80.2759768 147.38644
## 2005.4219 33.99493 -40.50738678 108.49724 -79.9465295 147.93638
## 2005.4247 32.81941 -41.75492378 107.39374 -81.2321903 146.87101
## 2005.4274 32.51460 -42.13167816 107.16088 -81.6470318 146.67624
## 2005.4301 32.94550 -41.77265443 107.66366 -81.3260585 147.21707
## 2005.4329 33.28041 -41.50955919 108.07038 -81.1009771 147.66180
## 2005.4356 33.92599 -40.93571802 108.78770 -80.5651133 148.41710
## 2005.4384 33.27267 -41.66071257 108.20605 -81.3280488 147.87339
## 2005.4411 33.49552 -41.50946089 108.50051 -81.2147019 148.20575
## 2005.4438 33.17568 -41.90084180 108.25220 -81.6439514 147.99531
## 2005.4466 32.94135 -42.20664169 108.08934 -81.9875839 147.87028
## 2005.4493 33.06158 -42.15780430 108.28097 -81.9765431 148.09971
## 2005.4521 33.92229 -41.36842596 109.21301 -81.2249255 149.06951
## 2005.4548 32.91469 -42.44729009 108.27668 -82.3415147 148.17090
## 2005.4575 32.56952 -42.86365833 108.00270 -82.7955723 147.93462
## 2005.4603 33.65607 -41.84824488 109.16038 -81.8178127 149.12994
## 2005.4630 33.67842 -41.89694933 109.25380 -81.9041356 149.26098
## 2005.4658 33.45668 -42.18969207 109.10305 -82.2344614 149.14782
## 2005.4685 34.09710 -41.62020438 109.81439 -81.7025215 149.89671
## 2005.4712 34.21924 -41.56892273 110.00740 -81.6887526 150.12723
## 2005.4740 34.35679 -41.50217231 110.21575 -81.6594798 150.37305
## 2005.4767 34.02227 -41.90741843 109.95196 -82.1021686 150.14671
## 2005.4795 34.53089 -41.46946422 110.53125 -81.7016223 150.76341
## 2005.4822 34.78040 -41.29055939 110.85135 -81.5600906 151.12088
## 2005.4849 34.53557 -41.60591929 110.67706 -81.9127889 150.98393
## 2005.4877 34.28228 -41.92967885 110.49424 -82.2738524 150.83841
## 2005.4904 34.52241 -41.75995602 110.80477 -82.1413990 151.18621
## 2005.4932 35.11934 -41.23335985 111.47204 -81.6520379 151.89072
## 2005.4959 35.21505 -41.20792340 111.63803 -81.6638023 152.09390
## 2005.4986 34.52594 -41.96724352 111.01912 -82.4602890 151.51217
## 2005.5014 34.36932 -42.19400584 110.93265 -82.7241839 151.46283
## 2005.5041 34.58571 -42.04770350 111.21912 -82.6149801 151.78639
## 2005.5068 34.33396 -42.36946576 111.03739 -82.9738070 151.64173
## 2005.5096 34.22226 -42.55111846 110.99564 -83.1924906 151.63701
## 2005.5123 34.56059 -42.28267540 111.40386 -82.9610446 152.08223
## 2005.5151 34.66400 -42.24909094 111.57710 -82.9644237 152.29243
## 2005.5178 34.70945 -42.27341158 111.69230 -83.0256744 152.44456
## 2005.5205 34.44202 -42.61054110 111.49457 -83.3997004 152.28373
## 2005.5233 34.73400 -42.38818816 111.85620 -83.2142107 152.68222
## 2005.5260 34.52637 -42.66539345 111.71814 -83.5282460 152.58099
## 2005.5288 34.51031 -42.75096569 111.77159 -83.6506150 152.67124
## 2005.5315 34.17055 -43.16017786 111.50127 -84.0965909 152.43769
## 2005.5342 33.86918 -43.53092912 111.26929 -84.5040729 152.24244
## 2005.5370 34.45938 -43.01005817 111.92881 -84.0198998 152.93865
## 2005.5397 35.04309 -42.49560445 112.58179 -83.5421111 153.62830
## 2005.5425 34.65573 -42.95216868 112.26363 -84.0353076 153.34676
## 2005.5452 33.70113 -43.97590065 111.37817 -85.0956393 152.49791
## 2005.5479 34.08637 -43.65974171 111.83248 -84.8160475 152.98879
## 2005.5507 33.22014 -44.59499121 111.03526 -85.7878316 152.22810
## 2005.5534 33.36215 -44.52192987 111.24623 -85.7512726 152.47558
## 2005.5562 33.56557 -44.38740724 111.51854 -85.6532200 152.78436
## 2005.5589 34.24965 -43.77216319 112.27145 -85.0744137 153.57370
## 2005.5616 34.49290 -43.59768352 112.58348 -84.9363397 153.92213
## 2005.5644 33.86433 -44.29496048 112.02362 -85.6699903 153.39865
## 2005.5671 34.21427 -44.01367744 112.44221 -85.4250490 153.85358
## 2005.5699 34.51754 -43.77899430 112.81407 -85.2266757 154.26175
## 2005.5726 34.45110 -43.91396118 112.81617 -85.3979206 154.30013
## 2005.5753 34.71092 -43.72261571 113.14446 -85.2428215 154.66466
## 2005.5781 34.52445 -43.97749508 113.02640 -85.5339156 154.58282
## 2005.5808 33.84145 -44.72885296 112.41174 -86.3214567 154.00435
## 2005.5836 33.84735 -44.79124172 112.48594 -86.4199972 154.11470
## 2005.5863 34.15946 -44.54736065 112.86629 -86.2122365 154.53116
## 2005.5890 34.48478 -44.29021787 113.25978 -85.9911828 154.96074
## 2005.5918 34.37644 -44.46667782 113.21955 -86.2037007 154.95657
## 2005.5945 34.42376 -44.48740668 113.33493 -86.2604563 155.10798
## 2005.5973 34.22886 -44.75030832 113.20803 -86.5593537 155.01707
## 2005.6000 34.14968 -44.89742367 113.19679 -86.7424338 155.04180
## 2005.6027 33.55321 -45.56178090 112.66819 -87.4427249 154.54914
## 2005.6055 33.01051 -46.17229593 112.19332 -88.0891430 154.11017
## 2005.6082 32.69943 -46.55114236 111.95000 -88.5038618 153.90272
## 2005.6110 32.50444 -46.81384217 111.82272 -88.8024033 153.81128
## 2005.6137 33.27646 -46.10946767 112.66239 -88.1338399 154.68676
## 2005.6164 33.05548 -46.39803701 112.50900 -88.4581899 154.56916
## 2005.6192 32.47215 -47.04890611 111.99320 -89.1448093 154.08910
## 2005.6219 31.68214 -47.90638721 111.27067 -90.0380103 153.40230
## 2005.6247 31.49242 -48.16352945 111.14837 -90.3308421 153.31568
## 2005.6274 32.16547 -47.55783805 111.88879 -89.7608102 154.09176
## 2005.6301 32.45148 -47.33913471 112.24210 -89.5777362 154.48070
## 2005.6329 32.14579 -47.71207350 112.00366 -89.9862743 154.27786
## 2005.6356 32.77993 -47.14512854 112.70499 -89.4548987 155.01476
## 2005.6384 32.81377 -47.17842866 112.80596 -89.5237383 155.15127
## 2005.6411 33.25643 -46.80284417 113.31570 -89.1836635 155.69652
## 2005.6438 33.41547 -46.71082820 113.54177 -89.1271275 155.95806
## 2005.6466 32.65538 -47.53788678 112.84864 -89.9896364 155.30039
## 2005.6493 32.34972 -47.91045374 112.60990 -90.3976241 155.09707
## 2005.6521 32.17493 -48.15210133 112.50196 -90.6746629 155.02452
## 2005.6548 31.62662 -48.76721020 112.02045 -91.3251336 154.57838
## 2005.6575 31.31377 -49.14680241 111.77435 -91.7400582 154.36760
## 2005.6603 31.70802 -48.81924438 112.23529 -91.4478033 154.86384
## 2005.6630 31.14760 -49.44629718 111.74150 -92.1101301 154.40533
## 2005.6658 30.99661 -49.66386690 111.65709 -92.3629446 154.35617
## 2005.6685 31.20398 -49.52301980 111.93098 -92.2573132 154.66528
## 2005.6712 31.44393 -49.34954010 112.23740 -92.1190202 155.00688
## 2005.6740 30.55986 -50.30003046 111.41974 -93.1046684 154.22438
## 2005.6767 29.84914 -51.07710739 110.77538 -93.9168743 153.61515
## 2005.6795 30.51220 -50.48035199 111.50475 -93.3552191 154.37962
## 2005.6822 30.88390 -50.17490665 111.94270 -93.0848452 154.85264
## 2005.6849 30.75301 -50.37199041 111.87801 -93.3169718 154.82299
## 2005.6877 29.30193 -51.88921791 110.49307 -94.8692135 153.47307
## 2005.6904 29.30359 -51.95364169 110.56083 -94.9686230 153.57581
## 2005.6932 28.93462 -52.38864855 110.25789 -95.4385872 153.30783
## 2005.6959 28.63842 -52.75083218 110.02767 -95.8356998 153.11254
## 2005.6986 27.24644 -54.20874205 108.70162 -97.3285103 151.82139
## 2005.7014 27.21761 -54.30344828 108.73867 -97.4580890 151.89331
## 2005.7041 28.01493 -53.57195310 109.60181 -96.7614381 152.79129
## 2005.7068 28.33581 -53.31683456 109.98846 -96.5411357 153.21276
## 2005.7096 28.25290 -53.46546811 109.97126 -96.7245574 153.23035
## 2005.7123 27.58470 -54.19932849 109.36873 -97.4931780 152.66258
## 2005.7151 27.67943 -54.17020510 109.52907 -97.4987870 152.85766
## 2005.7178 29.08095 -52.83425046 110.99615 -96.1975368 154.35943
## 2005.7205 29.79034 -52.19035952 111.77105 -95.5883226 155.16901
## 2005.7233 29.90540 -52.14075616 111.95156 -95.5733683 155.38417
## 2005.7260 29.60713 -52.50443041 111.71869 -95.9716640 155.18592
## 2005.7288 26.43609 -55.74081427 108.61300 -99.2426418 152.11483
## 2005.7315 25.38571 -56.85649695 107.62791 -100.3928909 151.16431
## 2005.7342 26.23353 -56.07391827 108.54098 -99.6448512 152.11192
## 2005.7370 25.96302 -56.40962961 108.33566 -100.0150741 151.94111
## 2005.7397 27.14875 -55.28903724 109.58654 -98.9289661 153.22647
## 2005.7425 27.30707 -55.19580650 109.80995 -98.8701925 153.48434
## 2005.7452 28.03361 -54.53430419 110.60153 -98.2431201 154.31035
## 2005.7479 26.86605 -55.76685584 109.49896 -99.5100746 153.24218
## 2005.7507 27.11628 -55.58156915 109.81412 -99.3591637 153.59171
## 2005.7534 27.69460 -55.06813063 110.45733 -98.8800740 154.26928
## 2005.7562 26.46162 -56.36594384 109.28919 -100.2122092 153.13546
## 2005.7589 24.06916 -58.82318795 106.96152 -102.7037483 150.84208
## 2005.7616 23.34782 -59.60926429 106.30491 -103.5240930 150.21974
## 2005.7644 24.40858 -58.61318771 107.43035 -102.5622580 151.37942
## 2005.7671 25.29966 -57.78674465 108.38606 -101.7700298 152.36935
## 2005.7699 26.80589 -56.34509669 109.95688 -100.3625702 153.97435
## 2005.7726 28.42633 -54.78919203 111.64185 -98.8408273 155.69348
## 2005.7753 28.45967 -54.82033623 111.73967 -98.9061068 155.82544
## 2005.7781 27.98128 -55.36316026 111.32571 -99.4830398 155.44559
## 2005.7808 26.41156 -56.99725831 109.82038 -101.1512204 153.97434
## 2005.7836 26.16925 -57.30389900 109.64241 -101.4919174 153.83043
## 2005.7863 26.11669 -57.42075293 109.65412 -101.6428013 153.87617
## 2005.7890 24.65721 -58.94445961 108.25889 -103.2005119 152.51494
## 2005.7918 24.14158 -59.52427778 107.80744 -103.8143078 152.09747
## 2005.7945 24.02966 -59.70033744 107.75965 -104.0243192 152.08363
## 2005.7973 24.26027 -59.53381215 108.05435 -103.8917197 152.41226
## 2005.8000 26.01220 -57.84591573 109.87032 -102.2377230 154.26213
## 2005.8027 27.12352 -56.79859262 111.04563 -101.2242739 155.47131
## 2005.8055 26.30034 -57.68571343 110.28639 -102.1452428 154.74592
## 2005.8082 25.94620 -58.10373987 109.99614 -102.5970916 154.48950
## 2005.8110 25.15128 -58.96250857 109.26506 -103.4896570 153.79221
## 2005.8137 25.16164 -59.01593691 109.33922 -103.5768564 153.90014
## 2005.8164 24.55142 -59.68990759 108.79275 -104.2845726 153.38741
## 2005.8192 24.17858 -60.12644658 108.48361 -104.7548316 153.11199
## 2005.8219 21.91674 -62.45193808 106.28541 -107.1140176 150.94749
## 2005.8247 22.38637 -62.04590973 106.81865 -106.7416583 151.51440
## 2005.8274 23.31825 -61.17758031 107.81409 -105.9069727 152.54348
## 2005.8301 24.54557 -60.01377050 109.10491 -104.7767813 153.86792
## 2005.8329 21.92996 -62.69283837 106.55276 -107.4894425 151.34936
## 2005.8356 19.74903 -64.93717988 104.43524 -109.7673520 149.26541
## 2005.8384 22.37106 -62.37851113 107.12064 -107.2422262 151.98435
## 2005.8411 24.90459 -59.90830468 109.71748 -104.8055377 154.61471
## 2005.8438 22.39975 -62.47641163 107.27591 -107.4071375 152.20664
## 2005.8466 19.78895 -65.15043790 104.72833 -110.1146318 149.69252
## 2005.8493 20.16906 -64.83349880 105.17162 -109.8311357 150.16926
## 2005.8521 19.88838 -65.17730674 104.95407 -110.2083619 149.98512
## 2005.8548 20.54781 -64.58096331 105.67658 -109.6454119 150.74102
## 2005.8575 22.08421 -63.10759856 107.27601 -108.2054158 152.37383
## 2005.8603 24.79758 -60.45721441 110.05237 -105.5883757 155.18353
## 2005.8630 21.58510 -63.73263750 106.90283 -108.8971182 152.06731
## 2005.8658 19.51064 -65.86999083 104.89127 -111.0677664 150.08905
## 2005.8685 20.23679 -65.20668503 105.68027 -110.4377310 150.91132
## 2005.8712 19.88132 -65.62496131 105.38760 -110.8892531 150.65190
## 2005.8740 20.64938 -64.91965470 106.21842 -110.2171680 151.51594
## 2005.8767 19.93514 -65.69661042 105.56689 -111.0273209 150.89760
## 2005.8795 18.69222 -67.00219269 104.38664 -112.3660760 149.75052
## 2005.8822 19.87604 -65.88099056 105.63308 -111.2780225 151.03011
## 2005.8849 20.17560 -65.64400705 105.99521 -111.0741634 151.42537
## 2005.8877 20.09857 -65.78356887 105.98070 -111.2468255 151.44396
## 2005.8904 20.45215 -65.49247174 106.39677 -110.9888046 151.89310
## 2005.8932 21.63795 -64.36910211 107.64501 -109.8984871 153.17439
## 2005.8959 20.38060 -65.68884646 106.45005 -111.2512597 152.01246
## 2005.8986 19.90285 -66.22894838 106.03464 -111.8243659 151.63006
## 2005.9014 20.07142 -66.12267442 106.26552 -111.7510723 151.89391
## 2005.9041 19.48117 -66.77518558 105.73752 -112.4365401 151.39887
## 2005.9068 19.36476 -66.95380662 105.68332 -112.6480939 151.37761
## 2005.9096 21.76021 -64.62052042 108.14094 -110.3477168 153.86814
## 2005.9123 22.12976 -64.31309447 108.57261 -110.0731763 154.33269
## 2005.9151 18.56448 -67.94045204 105.06941 -113.7333957 150.86235
## 2005.9178 17.62145 -68.94551014 104.18842 -114.7712920 150.01420
## 2005.9205 18.14078 -68.48817456 104.76973 -114.3467712 150.62832
## 2005.9233 20.93677 -65.75412688 107.62766 -111.6455148 153.51905
## 2005.9260 18.99173 -67.76106574 105.74452 -113.6852215 151.66868
## 2005.9288 19.15340 -67.66124847 105.96805 -113.6181487 151.92495
## 2005.9315 16.36170 -70.51476752 103.23816 -116.5043890 149.22778
## 2005.9342 16.44368 -70.49454805 103.38191 -116.5168674 149.40423
## 2005.9370 17.20845 -69.79150478 104.20840 -115.8464988 150.26340
## 2005.9397 19.26835 -67.79328855 106.32998 -113.8809341 152.41763
## 2005.9425 19.16184 -67.96142747 106.28512 -114.0817015 152.40539
## 2005.9452 17.72538 -69.45948090 104.91025 -115.6123602 151.06313
## 2005.9479 18.03385 -69.21255989 105.28027 -115.3980216 151.46573
## 2005.9507 16.50794 -70.79997740 103.81586 -117.0179984 150.03388
## 2005.9534 16.33963 -71.02975335 103.70901 -117.2803108 149.95957
## 2005.9562 17.17020 -70.26060311 104.60100 -116.5436742 150.88407
## 2005.9589 16.35632 -71.13585910 103.84850 -117.4514209 150.16406
## 2005.9616 15.77002 -71.78348807 103.32354 -118.1315178 149.67157
## 2005.9644 15.32870 -72.28610627 102.94350 -118.6665813 149.32397
## 2005.9671 13.77887 -73.89717705 101.45492 -120.3100746 147.86782
## 2005.9699 14.25122 -73.48603906 101.98847 -119.9313365 148.43377
## 2005.9726 14.38582 -73.41259587 102.18424 -119.8902707 148.66191
## 2005.9753 15.38716 -72.47237843 103.24670 -118.9824080 149.75673
## 2005.9781 17.05263 -70.86798452 104.97324 -117.4103464 151.51561
## 2005.9808 18.41813 -69.56351869 106.39978 -116.1381905 152.97445
## 2005.9836 19.54626 -68.49638164 107.58890 -115.1033409 154.19586
## 2005.9863 15.81055 -72.29304441 103.91414 -118.9322688 150.55336
## 2005.9890 16.28706 -71.87743560 104.45156 -118.5489027 151.12303
## 2005.9918 17.03439 -71.19098021 105.25975 -117.8946679 151.96344
## 2005.9945 18.75844 -69.52774764 107.04463 -116.2636337 153.78052
## 2005.9973 20.30549 -68.04148557 108.65246 -114.8095478 155.42052
## 2006.0000 20.01323 -68.39448185 108.42094 -115.1946981 155.22116
## 2006.0027 20.16132 -68.30708954 108.62973 -115.1394377 155.46208
## 2006.0055 18.79990 -69.72916499 107.32897 -116.5936231 154.19343##NOTE: AIC = 20992.54, BIC = 21009.62 , RMSE = 2.55584 Also, the headline of the plot below contains ETS(A,N,N) showing that the automated model characterized error of the “tsWSR_PK” SERIES as Additative (A), trend as None (A) and seasonality as None (N) which is equivalent to simple exponential model(ses) with only alpha parameter i.e level.
#Model 2 : ARIMA Model(AutoRegressive Moving Average)
#Changing to stationary set
train.sta_Var3 <- diff(train2, diff = 1)
test.sta_Var3 <- diff(test2, diff = 1)#2.1 Auto Arima model without sesonality:
set.seed(301)
model_Var3 <- auto.arima(train.sta_Var3, seasonal = FALSE)
summary(model_Var3)## Series: train.sta_Var3
## ARIMA(2,0,2) with zero mean
##
## Coefficients:
## ar1 ar2 ma1 ma2
## 0.6678 -0.2397 -0.7097 -0.1307
## s.e. 0.0635 0.0498 0.0649 0.0613
##
## sigma^2 estimated as 6.55: log likelihood=-5168.65
## AIC=10347.3 AICc=10347.33 BIC=10375.76
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -0.0005861283 2.557022 1.781308 NaN Inf 0.613599 -3.50044e-05##NOTE: AIC = 10347.3, BIC = 10375.76 , RMSE = 2.557022
tsdisplay(residuals(model_Var3), lag.max = 45, main = '(1,1,1) Model Residuals')
#2.2 Auto Arima model with sesonality:
set.seed(301)
model2_Var3 <- auto.arima(train.sta_Var3, seasonal= TRUE)
summary(model2_Var3)## Series: train.sta_Var3
## ARIMA(5,0,1) with zero mean
##
## Coefficients:
## ar1 ar2 ar3 ar4 ar5 ma1
## 0.8030 -0.3648 0.0437 0.0029 -0.0287 -0.8449
## s.e. 0.0332 0.0274 0.0304 0.0277 0.0244 0.0257
##
## sigma^2 estimated as 6.552: log likelihood=-5167.89
## AIC=10349.78 AICc=10349.84 BIC=10389.63
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -0.0005409411 2.556135 1.778874 NaN Inf 0.6127603 -0.0007242331##NOTE: AIC = 10349.78, BIC =10389.63 , RMSE = 2.556135
tsdisplay(residuals(model2_Var3), lag.max = 20, main = 'Seasonal Model Residuals')
NOTE: Above Graphs shows serious lags at 14. #2.3 Manual Arima
set.seed(301)
model1_Var3 <- arima(train.sta_Var3, order = c(2,0,14))
summary(model1_Var3)##
## Call:
## arima(x = train.sta_Var3, order = c(2, 0, 14))
##
## Coefficients:
## ar1 ar2 ma1 ma2 ma3 ma4 ma5 ma6
## 0.3552 -0.3002 -0.3929 -0.0841 -0.1333 -0.087 -0.0391 -0.0388
## s.e. 0.2875 0.1964 0.2871 0.1975 0.1147 0.107 0.0578 0.0265
## ma7 ma8 ma9 ma10 ma11 ma12 ma13 ma14
## 0.0653 -0.0673 0.0302 0.0497 -0.0241 0.0883 -0.0470 -0.0530
## s.e. 0.0242 0.0290 0.0292 0.0241 0.0297 0.0257 0.0299 0.0283
## intercept
## -0.0004
## s.e. 0.0153
##
## sigma^2 estimated as 6.418: log likelihood = -5148.33, aic = 10332.66
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 0.001016119 2.533326 1.770402 NaN Inf 0.6922123 0.0001662007##NOTE: AIC = 10332.66, RMSE = 2.533326
tsdisplay(residuals(model1_Var3), lag.max = 20, main = 'Seasonal Model Residuals')
Fit the observed with the predicted values for both models in the same plot.
par(mfrow = c(2,2))
fit_auto_train_Var3 %>% forecast(h=341) %>% autoplot() 
model1_Var3 %>% forecast(h=341) %>% autoplot() 
model2_Var3 %>% forecast(h=341) %>% autoplot() 
model_Var3 %>% forecast(h=341) %>% autoplot() 
COMMENT:
1. The plots includes 80% to 95% confidence interval.
2. For ARIMA models it plots the forecast but because of the nature of autoregressive process of lag, these forecast stabilizes quite smoothly.
Plot and comment on the residuals of the fitted data for both models in the same plot.
Residual Plot - to confirm no problem with this model
par(mfrow= c(2,2))
hist(fit_auto_train_Var3$residuals,col = 'red',xlab = 'Error',main = 'Histogram Of Residuals',freq= FALSE)
lines(density(fit_auto_train_Var3$residuals))
hist(model_Var3$residuals,col = 'red',xlab = 'Error',main = 'Histogram Of Residuals',freq= FALSE)
lines(density(model_Var3$residuals))
hist(model1_Var3$residuals,col = 'red',xlab = 'Error',main = 'Histogram Of Residuals',freq= FALSE)
lines(density(model1_Var3$residuals))
hist(model2_Var3$residuals,col = 'red',xlab = 'Error',main = 'Histogram Of Residuals',freq= FALSE)
lines(density(model2_Var3$residuals))
OBSERVATION: The residuals for each model are normally distributed, which shows the good fit of the models. It is normally distrbuted
Testing the autocorrelation and partial autocorrelation of the residuals (using the plots and Ljung-Box Q statistic) up to an appropriate lag *
- ACF & PACF Plots
par(mfrow = c(4,2))
acf(fit_auto_train_Var3$residuals, main = 'Correlogram')
pacf(fit_auto_train_Var3$residuals, main = 'Partial Corelogram')
acf(model_Var3$residuals, main = 'Correlogram')
pacf(model_Var3$residuals, main = 'Partial Corelogram')
acf(model1_Var3$residuals, main = 'Correlogram')
pacf(model1_Var3$residuals, main = 'Partial Corelogram')
acf(model2_Var3$residuals, main = 'Correlogram')
pacf(model2_Var3$residuals, main = 'Partial Corelogram')
NOTE: 1. Residuals are the difference between actaual and fitted values 2. These blue lines are signficance bounds 3. This graph shows us the autocorelations for insample forecast errors 4. Do not exceed these significance bounds for lags 1 to end
- Ljunx-Box Test to check the autocorelations of the residuals
Box.test(model_Var3$residuals, lag =20, type = 'Ljung-Box')##
## Box-Ljung test
##
## data: model_Var3$residuals
## X-squared = 50.734, df = 20, p-value = 0.0001737Box.test(model1_Var3$residuals, lag =20, type = 'Ljung-Box')##
## Box-Ljung test
##
## data: model1_Var3$residuals
## X-squared = 8.9669, df = 20, p-value = 0.9833Box.test(model2_Var3$residuals, lag =20, type = 'Ljung-Box')##
## Box-Ljung test
##
## data: model2_Var3$residuals
## X-squared = 49.345, df = 20, p-value = 0.0002747OBSERVATIONS: For above performed Ljunx-Box Test on model_Var3,model1_Var3 and model2_Var3 output, we can say that p-value is more than significance level 0.05 for model1_Var3.
Hence there is not a statistical significance.
We conclude that there is a liitle evidence of non-zero auto-corelations in the insample forecast errors at lags 1 to 20 model1_Var3.
So we fail to rejects the null hypothesis. Hence, we conclude that there is no serial auto corelation present between lags. Hence, the model_Var3 seems to be good fit compared to other models.
Test and comment on the normality of the residuals.
Here, further testing the normality by plotting Normal Q-Q plots. From below plots we observed that most of the datapoints lies on the line. Hence, we could conclude that our model produces residuals that are normal
par(mfrow = c(2,2))
qqnorm(fit_auto_train_Var3$residuals)
qqnorm(model_Var3$residuals)
qqnorm(model1_Var3$residuals)
qqnorm(model2_Var3$residuals)
Validating The Model by testing the model performance with Holdout set
Here, choosing RMSE as evaluation parameter. The lower RMSE indicates a more accurate forecast.
Below, is the comparison of model. We are fitting the model to test set which is the holdout set. And checking the accuracy using RMSE(Root mean square error) evaluation parameter.
accuracy(forecast(fit_auto_train_Var3), test2) ["Test set", "RMSE"]## [1] 6.973589#o/p - 6.973589
accuracy(forecast(model1_Var3), test.sta_Var3) ["Test set", "RMSE"]## [1] 2.481816#O/P - 2.481816
accuracy(forecast(model2_Var3), test.sta_Var3) ["Test set", "RMSE"]## [1] 2.479714#o/p - 2.479714
accuracy(forecast(model_Var3), test.sta_Var3) ["Test set", "RMSE"]## [1] 2.479376#O/P - 2.479376
NOTE:- Here, the RMSE value is less of ARIMA models compared to exponential model.
The minimum RMSE is of model_Var3.
COMMENT ON BEST MODEL AND ITS PARAMETERS
We observed the best model to be ARIMA model i.e.“model_Var3”.
summary(model_Var3)## Series: train.sta_Var3
## ARIMA(2,0,2) with zero mean
##
## Coefficients:
## ar1 ar2 ma1 ma2
## 0.6678 -0.2397 -0.7097 -0.1307
## s.e. 0.0635 0.0498 0.0649 0.0613
##
## sigma^2 estimated as 6.55: log likelihood=-5168.65
## AIC=10347.3 AICc=10347.33 BIC=10375.76
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -0.0005861283 2.557022 1.781308 NaN Inf 0.613599 -3.50044e-05Auto Arima Model(2,0,2) is the best model,which means
p = 2,
d = 0
q = 2
For the best model, 2 member of lag is used as a predictor. As we transformed the series to stationary so members of differences needed for stationarity is 0. 2 are the number of lagged forecasts errors used in the prediction equation.
AICc- Means AIC with correction is equaivalent to 10347.33.
AIC = 10347.33, RMSE = 2.557022 which is minimum as compared to other models.
4. Forecasting on T at 850 hpa level (or about 1500 m height) (T85)
#Checking the attributes of time series
attributes(tsT85)## $tsp
## [1] 1998.00 2004.94 365.00
##
## $class
## [1] "ts"#Plotting the series
plot(tsT85, main = "T at 850 hpa level (or about 1500 m height)(tsT85)", col = "red")
From the plot, we observes that there is no trend but seems to have seasonlity.
By just looking, it doesnt seems that data is missing.
Checking the statistics and visualising the missing data in the series:
plotNA.distribution(tsT85)
NOTE: Here, Data is missing at random
As we see the data is missing randomly, so locf and NOCB does seems the good technique to implement here.
#Impute the missing values with “na_locf” function of “imputeTS package” and visualise the imputed values in the time series
tsT85.imp <- na_locf(tsT85)
plotNA.imputations(tsT85, tsT85.imp)
#Decomposition Of Time Series
decomp3 <- decompose(tsT85.imp)
plot(decomp3, col = "red")
OBSERVATIONS:
1)There seems to have trend.
2)It seems to have downward trend.
3)We observe some seasonality in the series. Seasonality describes cyclical effects due to the time of the year.
Let’s explore this seasonality pattern by plotting the decomp$seasonal components such that y-axis represents Seasonality Index and x-axis has month
par(mfrow=c(1,2))
plot(decomp3$seasonal, type ='b', xlab = 'Years', ylab = 'Seasonality Index', col = 'blue', las = 2, main = "SEASONAL DATA")
plot(decomp3$seasonal[1:365], type ='b', xlab = 'Years', ylab = 'Seasonality Index', col = 'blue', las = 2, main = "SEASONAL DATA")
OBSERVATIONS:
1) There is increase in the mid of months of a year.
2) There is a drop in peak T for starting and ending months of the year
#Stationarity check of time series
We could check the stationarity of time series by ADF and KPSS Tests:
- Augmented Dickey- Fuller(ADF) t-statistic test for unit root
- Kwiatkowski-Phillips-Schmidt-Shin (KPSS) for level or trend stationarity
adf.test(tsT85.imp)## Warning in adf.test(tsT85.imp): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: tsT85.imp
## Dickey-Fuller = -4.4455, Lag order = 13, p-value = 0.01
## alternative hypothesis: stationaryNOTE: Here p-value is less, so the series is stationary
kpss.test(tsT85.imp, null="Trend")##
## KPSS Test for Trend Stationarity
##
## data: tsT85.imp
## KPSS Trend = 0.15198, Truncation lag parameter = 8, p-value = 0.04502NOTE: Here p-value is less, so the series is not stationary
Plotting ACF to check the auto-corelations
acf(tsT85.imp,lag.max = length(tsT85.imp),xlab = "lag #", ylab = 'ACF',main='Statiionary Check ')
Here, we observes most of the data lies outside the blue-dotted lines means the significance level.
Now, we will take the difference to make our data stationary.
It seems difference of 1 is sufficient to make the series stationary.
tsT85.sta <- diff(tsT85.imp)
attributes(tsT85.sta)## $tsp
## [1] 1998.003 2004.940 365.000
##
## $class
## [1] "ts"Hence, after differencing our series is now transformed to stationary time series.
#Visualising the stationary series
acf(tsT85.sta, lag.max = length(tsT85.sta),xlab = "lag #", ylab = 'ACF',main='Statiionary Check ')
#CREATING MODELS AND FORECASTING: USING EXPONENTIAL SMOOTHING AND ARIMA TECHNIQUES FOR TIME SERIES FORECASTING
1.Train - Test Split of the data
train3 <- window(tsT85.imp, end = c(2004, 3))
test3 <- window(tsT85.imp, start = c(2004, 4))#Model 1 : Auto Exponential Smoothening Model
set.seed(301)
fit_auto_train_Var4 <- forecast(train3)
summary(fit_auto_train_Var4)##
## Forecast method: STL + ETS(A,N,N)
##
## Model Information:
## ETS(A,N,N)
##
## Call:
## ets(y = na.interp(x), model = etsmodel, allow.multiplicative.trend = allow.multiplicative.trend)
##
## Smoothing parameters:
## alpha = 0.8933
##
## Initial states:
## l = 11.8188
##
## sigma: 2.0766
##
## AIC AICc BIC
## 20079.90 20079.91 20096.98
##
## Error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set 0.00241468 2.075702 1.44361 -4.866176 27.31777 0.4473464
## ACF1
## Training set 0.02562371
##
## Forecasts:
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 2004.0082 11.100237 8.43890376 13.76157 7.03007890 15.17040
## 2004.0110 10.869974 7.30136062 14.43859 5.41225055 16.32770
## 2004.0137 12.370131 8.08208803 16.65817 5.81213512 18.92813
## 2004.0164 12.962118 8.05909656 17.86514 5.46359361 20.46064
## 2004.0192 10.732447 5.28341641 16.18148 2.39887400 19.06602
## 2004.0219 10.696135 4.75103263 16.64124 1.60388561 19.78838
## 2004.0247 10.808086 4.40523086 17.21094 1.01576428 20.60041
## 2004.0274 13.228469 6.39847236 20.05847 2.78289038 23.67405
## 2004.0301 12.859264 5.62730893 20.09122 1.79894343 23.91958
## 2004.0329 12.738680 5.12596149 20.35140 1.09603199 24.38133
## 2004.0356 11.767162 3.79183806 19.74249 -0.43004318 23.96437
## 2004.0384 12.672229 4.35008387 20.99437 -0.05539346 25.39985
## 2004.0411 12.935372 4.28029212 21.59045 -0.30143025 26.17217
## 2004.0438 14.177364 5.20169069 23.15304 0.45025624 27.90447
## 2004.0466 10.797635 1.51243078 20.08284 -3.40285951 24.99813
## 2004.0493 11.810703 2.22595799 21.39545 -2.84789932 26.46930
## 2004.0521 12.395595 2.52039205 22.27080 -2.70722475 27.49842
## 2004.0548 11.255144 1.09778496 21.41250 -4.27919623 26.78948
## 2004.0575 11.820608 1.38872131 22.25249 -4.13358583 27.77480
## 2004.0603 10.189616 -0.50975665 20.88899 -6.17366214 26.55289
## 2004.0630 9.907523 -1.05280901 20.86785 -6.85485820 26.66990
## 2004.0658 12.506252 1.29103136 23.72147 -4.64594802 29.65845
## 2004.0685 11.231639 -0.23280583 22.69608 -6.30171624 28.76499
## 2004.0712 9.151921 -2.55644404 20.86029 -8.75447784 27.05832
## 2004.0740 12.895457 0.94815189 24.84276 -5.37636963 31.16728
## 2004.0767 13.498790 1.31722966 25.68035 -5.13129898 32.12888
## 2004.0795 12.977617 0.56622225 25.38901 -6.00397341 31.95921
## 2004.0822 13.081694 0.44464409 25.71874 -6.24500616 32.40839
## 2004.0849 13.364708 0.50596219 26.22345 -6.30104668 33.03046
## 2004.0877 12.422666 -0.65401764 25.49935 -7.57639578 32.42173
## 2004.0904 14.367918 1.07687024 27.65897 -5.95898568 34.69482
## 2004.0932 13.545399 0.04338924 27.04741 -7.10414306 34.19494
## 2004.0959 12.674579 -1.03514700 26.38430 -8.29263743 33.64179
## 2004.0986 12.870449 -1.04389239 26.78479 -8.40969966 34.15060
## 2004.1014 12.596089 -1.51990159 26.71208 -8.99245577 34.18463
## 2004.1041 11.758253 -2.55654707 26.07305 -10.13434460 33.65085
## 2004.1068 12.536246 -1.97464009 27.04713 -9.65623919 34.72873
## 2004.1096 12.058714 -2.64564319 26.76307 -10.42965977 34.54709
## 2004.1123 10.818531 -4.07678469 25.71385 -11.96188859 33.59895
## 2004.1151 13.143482 -1.94037523 28.22734 -9.92528681 36.21225
## 2004.1178 14.085787 -1.18428324 29.35586 -9.26777026 37.43934
## 2004.1205 13.683871 -1.77016901 29.13791 -9.95104376 37.31879
## 2004.1233 11.651619 -3.98422644 27.28746 -12.26134314 35.56458
## 2004.1260 11.477994 -4.33756725 27.29356 -12.70981966 35.66581
## 2004.1288 11.616076 -4.37718159 27.60933 -12.84350073 36.07565
## 2004.1315 13.957130 -2.21187143 30.12613 -10.77122357 38.68548
## 2004.1342 13.114389 -3.22846588 29.45724 -11.87985065 38.10863
## 2004.1370 10.389784 -6.12509410 26.90466 -14.86754272 35.64711
## 2004.1397 11.101115 -5.58401413 27.78624 -14.41658777 36.61882
## 2004.1425 12.268456 -4.58520314 29.12212 -13.50699145 38.04390
## 2004.1452 12.414861 -4.60566012 29.43538 -13.61577977 38.44550
## 2004.1479 13.675931 -3.50983185 30.86169 -12.60742523 39.95929
## 2004.1507 14.597821 -2.75160981 31.94725 -11.93584384 41.13149
## 2004.1534 13.834977 -3.67659289 31.34655 -12.94665784 40.61661
## 2004.1562 13.069035 -4.60318592 30.74126 -13.95829433 40.09636
## 2004.1589 11.800443 -6.03098100 29.63187 -15.47036672 39.07125
## 2004.1616 12.848860 -5.14035852 30.83808 -14.66327573 40.36100
## 2004.1644 12.930553 -5.21508883 31.07619 -14.82081116 40.68192
## 2004.1671 13.077464 -5.22326314 31.37819 -14.91108286 41.06601
## 2004.1699 14.620315 -3.83419401 33.07482 -13.60342122 42.84405
## 2004.1726 14.692896 -3.91412513 33.29992 -13.76408704 43.14988
## 2004.1753 14.270794 -4.48749851 33.02909 -14.41753874 42.95913
## 2004.1781 14.738626 -4.16972837 33.64698 -14.17920630 43.65646
## 2004.1808 11.857418 -7.19981560 30.91465 -17.28810573 41.00294
## 2004.1836 9.091919 -10.11304040 28.29688 -20.27953178 38.46337
## 2004.1863 9.914159 -9.43739808 29.26572 -19.68149377 39.50981
## 2004.1890 12.880308 -6.61674547 32.37736 -16.93786198 42.69848
## 2004.1918 13.535456 -6.10601483 33.17693 -16.50358163 43.57449
## 2004.1945 13.569903 -6.21493178 33.35474 -16.68839083 43.82820
## 2004.1973 13.771620 -6.15554796 33.69879 -16.70435330 44.24759
## 2004.2000 14.258552 -5.80993846 34.32704 -16.43355570 44.95066
## 2004.2027 14.964083 -5.24474229 35.17291 -15.94264829 45.87081
## 2004.2055 17.118255 -3.22993756 37.46645 -14.00161997 48.23813
## 2004.2082 16.635054 -3.85155771 37.12167 -14.69651467 47.96662
## 2004.2110 14.657036 -5.96706525 35.28114 -16.88480498 46.19888
## 2004.2137 13.368753 -7.39192727 34.12943 -18.38196777 45.11947
## 2004.2164 14.992072 -5.90429580 35.88844 -16.96616452 46.95031
## 2004.2192 15.548627 -5.48255178 36.57981 -16.61578532 47.71304
## 2004.2219 14.688821 -6.47631036 35.85395 -17.68045416 47.05810
## 2004.2247 13.925324 -7.37291753 35.22357 -18.64752562 46.49817
## 2004.2274 15.691895 -5.73863045 37.12242 -17.08326518 48.46705
## 2004.2301 16.003726 -5.55827125 37.56572 -16.97250299 48.97995
## 2004.2329 17.353855 -4.33881733 39.04653 -15.82222431 50.52993
## 2004.2356 16.781209 -5.04135616 38.60377 -16.59352415 50.15594
## 2004.2384 18.005325 -3.94636356 39.95701 -15.56688569 51.57754
## 2004.2411 17.256063 -4.82399528 39.33612 -16.51247183 51.02460
## 2004.2438 17.343729 -4.86395602 39.55141 -16.61999418 51.30745
## 2004.2466 16.668762 -5.66582062 39.00334 -17.48903434 50.82656
## 2004.2493 16.824957 -5.63580577 39.28572 -17.52581553 51.17573
## 2004.2521 18.180715 -4.40552392 40.76695 -16.36195656 52.72339
## 2004.2548 18.298618 -4.41240343 41.00964 -16.43489197 53.03213
## 2004.2575 17.518525 -5.31659756 40.35365 -17.40478105 52.44183
## 2004.2603 17.012144 -5.94640767 39.97070 -18.09993101 52.12422
## 2004.2630 17.713327 -5.36799476 40.79465 -17.58650853 53.01316
## 2004.2658 18.915166 -4.28827667 42.11861 -16.57143702 54.40177
## 2004.2685 17.588966 -5.73595696 40.91389 -18.08342543 53.26136
## 2004.2712 17.762945 -5.68282953 41.20872 -18.09427292 53.62016
## 2004.2740 17.878965 -5.68704104 41.44497 -18.16213128 53.92006
## 2004.2767 16.172771 -7.51285733 39.85840 -20.05127133 52.39681
## 2004.2795 15.560278 -8.24436977 39.36493 -20.84578933 51.96635
## 2004.2822 16.136639 -7.78643695 40.05972 -20.45054862 52.72383
## 2004.2849 16.661509 -7.37941215 40.70243 -20.10590710 53.42893
## 2004.2877 18.613103 -5.54508847 42.77129 -18.33366240 55.55987
## 2004.2904 19.773956 -4.50093913 44.04885 -17.35129214 56.89920
## 2004.2932 20.181792 -4.20924775 44.57283 -17.12108425 57.48467
## 2004.2959 20.157741 -4.34889333 44.66438 -17.32192193 57.63740
## 2004.2986 19.572442 -5.04924431 44.19413 -18.08317774 57.22806
## 2004.3014 18.427225 -6.30897770 43.16343 -19.40353268 56.25798
## 2004.3041 17.703779 -7.14641350 42.55397 -20.30131067 55.70887
## 2004.3068 18.020680 -6.94298043 42.98434 -20.15794425 56.19931
## 2004.3096 18.990083 -6.08653289 44.06670 -19.36129157 57.34146
## 2004.3123 18.675156 -6.51390846 43.86422 -19.84819388 57.19851
## 2004.3151 17.776550 -7.52446372 43.07756 -20.91801131 56.47111
## 2004.3178 17.508823 -7.90364660 42.92129 -21.35619529 56.37384
## 2004.3205 18.143298 -7.38013994 43.66674 -20.89143210 57.17803
## 2004.3233 18.356111 -7.27781626 43.99004 -20.84759757 57.55982
## 2004.3260 19.101355 -6.64258652 44.84530 -20.27060598 58.47332
## 2004.3288 18.540640 -7.31284748 44.39413 -20.99885727 58.08014
## 2004.3315 17.696061 -8.26651112 43.65863 -22.01026654 57.40239
## 2004.3342 17.992708 -8.07849131 44.06391 -21.87975076 57.86517
## 2004.3370 18.195672 -7.98370499 44.37505 -21.84222987 58.23357
## 2004.3397 20.025059 -6.26204987 46.31217 -20.17760452 60.22772
## 2004.3425 19.337963 -7.05643736 45.73236 -21.02878900 59.70472
## 2004.3452 18.636581 -7.86467728 45.13784 -21.89359598 59.16676
## 2004.3479 18.584852 -8.02283488 45.19254 -22.10809346 59.27780
## 2004.3507 19.183317 -7.53037415 45.89701 -21.67174816 60.03838
## 2004.3534 19.874027 -6.94524976 46.69330 -21.14251739 60.89057
## 2004.3562 19.796560 -7.12788874 46.72101 -21.38083081 60.97395
## 2004.3589 20.773392 -6.25581834 47.80260 -20.56421820 62.11100
## 2004.3616 20.159768 -6.97380093 47.29334 -21.33744448 61.65698
## 2004.3644 19.932499 -7.30502787 47.17003 -21.72370345 61.58870
## 2004.3671 20.076747 -7.26434271 47.41784 -21.73784107 61.89133
## 2004.3699 20.039185 -7.40507632 47.48345 -21.93319059 62.01156
## 2004.3726 20.056469 -7.49057731 47.60352 -22.07310293 62.18604
## 2004.3753 19.692924 -7.95652633 47.34237 -22.59326104 61.97911
## 2004.3781 19.807539 -7.94393654 47.55901 -22.63468030 62.24976
## 2004.3808 19.863035 -7.99009257 47.71616 -22.73464755 62.46072
## 2004.3836 21.277769 -6.67664032 49.23218 -21.47481085 64.03035
## 2004.3863 20.926291 -7.12903504 48.98162 -21.98062757 63.83321
## 2004.3890 21.059098 -7.09678248 49.21498 -22.00160552 64.11980
## 2004.3918 20.245526 -8.01055241 48.50160 -22.96841653 63.45947
## 2004.3945 19.612115 -8.74380541 47.96804 -23.75452320 62.97875
## 2004.3973 19.601465 -8.85394839 48.05688 -23.91733440 63.12026
## 2004.4000 19.975418 -8.57914104 48.52998 -23.69501175 63.64585
## 2004.4027 20.105230 -8.54813281 48.75859 -23.71630662 63.92677
## 2004.4055 20.201167 -8.55065862 48.95299 -23.77095580 64.17329
## 2004.4082 19.319197 -9.53075587 48.16915 -24.80299852 63.44139
## 2004.4110 20.635953 -8.31179504 49.58370 -23.63580707 64.90771
## 2004.4137 21.255782 -7.78943101 50.30100 -23.16503812 65.67660
## 2004.4164 21.229521 -7.91283130 50.37187 -23.33986094 65.79890
## 2004.4192 20.195248 -9.04392144 49.43442 -24.52220277 64.91270
## 2004.4219 20.377302 -8.95836476 49.71297 -24.48772863 65.24233
## 2004.4247 19.712661 -9.71918667 49.14451 -25.29946560 64.72479
## 2004.4274 19.661051 -9.86666449 49.18877 -25.49769264 64.81979
## 2004.4301 19.672858 -9.95041482 49.29613 -25.63202795 64.97774
## 2004.4329 19.799030 -9.91949281 49.51755 -25.65152827 65.24959
## 2004.4356 19.876861 -9.93660679 49.69033 -25.71890349 65.47263
## 2004.4384 20.734980 -9.17313273 50.64309 -25.00553111 66.47549
## 2004.4411 19.923246 -10.07921237 49.92570 -25.96155439 65.80805
## 2004.4438 19.890735 -10.20577285 49.98724 -26.13790194 65.91937
## 2004.4466 19.385694 -10.80457166 49.57596 -26.78633272 65.55772
## 2004.4493 19.706667 -10.57706467 49.99040 -26.60830405 66.02164
## 2004.4521 20.251052 -10.12585952 50.62796 -26.20642497 66.70853
## 2004.4548 20.365241 -10.10456431 50.83505 -26.23430500 66.96479
## 2004.4575 20.837822 -9.72459552 51.40024 -25.90336197 67.57901
## 2004.4603 20.355115 -10.29963469 51.00986 -26.52727880 67.23751
## 2004.4630 20.791813 -9.95499167 51.53862 -26.23136666 67.81499
## 2004.4658 21.191192 -9.64739186 52.02978 -25.97235226 68.35474
## 2004.4685 20.481799 -10.44829331 51.41189 -26.82169496 67.78529
## 2004.4712 20.739408 -10.28192152 51.76074 -26.70362152 68.18244
## 2004.4740 20.814072 -10.29822755 51.92637 -26.76808427 68.39623
## 2004.4767 21.115366 -10.08763858 52.31837 -26.60551161 68.83624
## 2004.4795 21.293893 -9.99955413 52.58734 -26.56530432 69.15309
## 2004.4822 21.384012 -9.99961671 52.76764 -26.61310606 69.38113
## 2004.4849 21.441909 -10.03164278 52.91546 -26.69273452 69.57655
## 2004.4877 21.297473 -10.26574508 52.86069 -26.97430358 69.56925
## 2004.4904 22.076523 -9.57610774 53.72915 -26.33199854 70.48505
## 2004.4932 22.195206 -9.54658599 53.93700 -26.34967576 70.74009
## 2004.4959 22.309310 -9.52139326 54.14001 -26.37154979 70.99017
## 2004.4986 22.291116 -9.62825074 54.21048 -26.52534293 71.10758
## 2004.5014 21.755836 -10.25194894 53.76362 -27.19584678 70.70752
## 2004.5041 22.035171 -10.06078828 54.13113 -27.05136283 71.12170
## 2004.5068 22.290169 -9.89372312 54.47406 -26.93084649 71.51118
## 2004.5096 21.530987 -10.74059793 53.80257 -27.82414329 70.88612
## 2004.5123 21.893317 -10.46572419 54.25236 -27.59556574 71.38220
## 2004.5151 22.143876 -10.30238515 54.59014 -27.47839810 71.76615
## 2004.5178 22.394683 -10.13856422 54.92793 -27.36062479 72.14999
## 2004.5205 22.093827 -10.52617342 54.71383 -27.79415881 71.98181
## 2004.5233 21.849357 -10.85716814 54.55588 -28.17095654 71.86967
## 2004.5260 21.190832 -11.60198873 53.98365 -28.96145930 71.34312
## 2004.5288 20.514867 -12.36402261 53.39376 -29.76905544 70.79879
## 2004.5315 21.043148 -11.92158580 54.00788 -29.37206193 71.45836
## 2004.5342 21.377299 -11.67305695 54.42765 -29.16885834 71.92346
## 2004.5370 21.305491 -11.83026477 54.44125 -29.37127431 71.98226
## 2004.5397 21.713465 -11.50747190 54.93440 -29.09357338 72.52050
## 2004.5425 22.009961 -11.29593815 55.31586 -28.92701623 72.94694
## 2004.5452 22.017628 -11.37301844 55.40827 -29.04895869 73.08421
## 2004.5479 21.492663 -11.98251545 54.96784 -29.70320430 72.68853
## 2004.5507 21.237449 -12.32204843 54.79695 -30.08737315 72.56227
## 2004.5534 20.897338 -12.74626683 54.54094 -30.55611557 72.35079
## 2004.5562 20.733311 -12.99419174 54.46081 -30.84845346 72.31508
## 2004.5589 21.173944 -12.63724872 54.98514 -30.53581320 72.88370
## 2004.5616 21.287553 -12.60712297 55.18223 -30.54988085 73.12499
## 2004.5644 21.741634 -12.23632082 55.71959 -30.22316350 73.70643
## 2004.5671 21.576427 -12.48460224 55.63746 -30.51542193 73.66828
## 2004.5699 21.894851 -12.24905047 56.03875 -30.32374019 74.11344
## 2004.5726 22.251280 -11.97529357 56.47785 -30.09374708 74.59631
## 2004.5753 21.906217 -12.40282896 56.21526 -30.56494081 74.37737
## 2004.5781 22.115503 -12.27581816 56.50682 -30.48148366 74.71249
## 2004.5808 22.023979 -12.44942020 56.49738 -30.69853541 74.74649
## 2004.5836 21.237686 -13.31759673 55.79297 -31.61005843 74.08543
## 2004.5863 21.576145 -13.06082780 56.21312 -31.39653353 74.54882
## 2004.5890 21.734275 -12.98419564 56.45274 -31.36304364 74.83159
## 2004.5918 22.001135 -12.79864259 56.80091 -31.22053183 75.22280
## 2004.5945 22.533583 -12.34731101 57.41448 -30.81214116 75.87931
## 2004.5973 22.749353 -12.21247069 57.71118 -30.72014213 76.21885
## 2004.6000 22.675904 -12.36666216 57.71847 -30.91707594 76.26888
## 2004.6027 22.027887 -13.09523535 57.15101 -31.68829321 75.74407
## 2004.6055 21.382274 -13.82122030 56.58577 -32.45682466 75.22137
## 2004.6082 20.633116 -14.65056787 55.91680 -33.32862182 74.59485
## 2004.6110 20.723915 -14.63977629 56.08761 -33.36018357 74.80801
## 2004.6137 21.165930 -14.27758796 56.60945 -33.04025297 75.37211
## 2004.6164 21.682840 -13.84032511 57.20601 -32.64515288 76.01083
## 2004.6192 21.741977 -13.86065748 57.34461 -32.70755369 76.19151
## 2004.6219 21.318824 -14.36310250 57.00075 -33.25197347 75.88962
## 2004.6247 20.329233 -15.43180952 56.09028 -34.36256217 75.02103
## 2004.6274 20.936372 -14.90361264 56.77636 -33.87615451 75.74890
## 2004.6301 21.981265 -13.93748793 57.90002 -32.95172719 76.91426
## 2004.6329 21.332651 -14.66469783 57.33000 -33.72054322 76.38585
## 2004.6356 21.078848 -14.99692500 57.15462 -34.09428589 76.25198
## 2004.6384 21.788416 -14.36561176 57.94244 -33.50439809 77.08123
## 2004.6411 21.821701 -14.41041277 58.05381 -33.59053508 77.23394
## 2004.6438 22.258517 -14.05151364 58.56855 -33.27288303 77.78992
## 2004.6466 22.189811 -14.19797113 58.57759 -33.46049928 77.84012
## 2004.6493 20.742659 -15.72270745 57.20803 -35.02630660 76.51163
## 2004.6521 20.844853 -15.69793368 57.38764 -35.04251662 76.73222
## 2004.6548 20.018382 -16.60166122 56.63843 -35.98714132 76.02391
## 2004.6575 20.533995 -16.16314254 57.23113 -35.58943369 76.65742
## 2004.6603 20.374670 -16.39939955 57.14874 -35.86641620 76.61576
## 2004.6630 20.189322 -16.66151975 57.04016 -36.16917688 76.54782
## 2004.6658 20.513849 -16.41360413 57.44130 -35.96181725 76.98952
## 2004.6685 20.345192 -16.65871520 57.34910 -36.24740034 76.93778
## 2004.6712 20.241127 -16.83907636 57.32133 -36.46815008 76.95040
## 2004.6740 19.755335 -17.40100668 56.91168 -37.07038603 76.58106
## 2004.6767 19.049696 -18.18262940 56.28202 -37.89223198 75.99162
## 2004.6795 19.229316 -18.07883845 56.53747 -37.82858232 76.28721
## 2004.6822 19.543842 -17.83998746 56.92767 -37.62979121 76.71747
## 2004.6849 19.571459 -17.88789223 57.03081 -37.71767492 76.86059
## 2004.6877 20.324329 -17.21039186 57.85905 -37.08007307 77.72873
## 2004.6904 18.867605 -18.74233572 56.47754 -38.65183547 76.38704
## 2004.6932 18.504384 -19.18062566 56.18939 -39.12986449 76.13863
## 2004.6959 19.234976 -18.52495258 56.99491 -38.51385148 76.98380
## 2004.6986 18.807392 -19.02730768 56.64209 -39.05578812 76.67057
## 2004.7014 18.841404 -19.06792038 56.75073 -39.13590429 76.81871
## 2004.7041 18.730012 -19.25378905 56.71381 -39.36119882 76.82122
## 2004.7068 18.593233 -19.46489987 56.65137 -39.61165833 76.79812
## 2004.7096 18.306417 -19.82590271 56.43874 -40.01193318 76.62477
## 2004.7123 17.458791 -20.74757044 55.66515 -40.97279665 75.89038
## 2004.7151 17.859130 -20.42113115 56.13939 -40.68547729 76.40374
## 2004.7178 18.141785 -20.21223316 56.49580 -40.51562387 76.79919
## 2004.7205 18.711876 -19.71575697 57.13951 -40.05811730 77.48187
## 2004.7233 18.225893 -20.27521467 56.72700 -40.65647010 77.10826
## 2004.7260 18.708023 -19.86641924 57.28247 -40.28649569 77.70254
## 2004.7288 18.945196 -19.70244190 57.59283 -40.16126571 78.05166
## 2004.7315 17.768960 -20.95173558 56.48965 -41.44923351 76.98715
## 2004.7342 17.730998 -21.06261687 56.52461 -41.59871607 77.06071
## 2004.7370 16.791329 -22.07506870 55.65773 -42.64969676 76.23235
## 2004.7397 16.936226 -22.00281808 55.87527 -42.61590298 76.48836
## 2004.7425 17.482168 -21.52938778 56.49372 -42.18085791 77.14519
## 2004.7452 18.189207 -20.89472531 57.27314 -41.58450946 77.96292
## 2004.7479 18.542392 -20.61378347 57.69857 -41.34181081 78.42660
## 2004.7507 17.627484 -21.60080148 56.85577 -42.36700158 77.62197
## 2004.7534 18.368852 -20.93141184 57.66912 -41.73571466 78.47342
## 2004.7562 16.596880 -22.77522985 55.96899 -43.61756574 76.81133
## 2004.7589 16.818755 -22.62507012 56.26258 -43.50536980 77.14288
## 2004.7616 16.522339 -22.99307083 56.03775 -43.91126540 76.95594
## 2004.7644 15.761034 -23.82583146 55.34790 -44.78185240 76.30392
## 2004.7671 16.854606 -22.80358722 56.51280 -43.79736637 77.50658
## 2004.7699 17.076627 -22.65276507 56.80602 -43.68423464 77.83749
## 2004.7726 16.584224 -23.21623952 56.38469 -44.28533208 77.45378
## 2004.7753 17.224579 -22.64682936 57.09599 -43.75347786 78.20264
## 2004.7781 17.092659 -22.84956836 57.03489 -43.99370609 78.17902
## 2004.7808 17.089652 -22.92326820 57.10257 -44.10482880 78.28413
## 2004.7836 17.660591 -22.42289798 57.74408 -43.64181546 78.96300
## 2004.7863 16.821719 -23.33221523 56.97565 -44.58842394 78.23186
## 2004.7890 16.114327 -24.10992802 56.33858 -45.40336264 77.63202
## 2004.7918 15.553872 -24.74058221 55.84833 -46.07117778 77.17892
## 2004.7945 16.219957 -24.14457405 56.58449 -45.51226594 77.95218
## 2004.7973 16.052219 -24.38226679 56.48671 -45.78699070 77.89143
## 2004.8000 15.216095 -25.28822490 55.72042 -46.72991689 77.16211
## 2004.8027 15.823018 -24.75101657 56.39705 -46.22961300 77.87565
## 2004.8055 16.069497 -24.57413234 56.71313 -46.08956992 78.22856
## 2004.8082 15.829887 -24.88321809 56.54299 -46.43543383 78.09521
## 2004.8110 15.771403 -25.01105851 56.55387 -46.59998977 78.14280
## 2004.8137 15.144422 -25.70727911 55.99612 -47.33286354 77.62171
## 2004.8164 14.861826 -26.05899767 55.78265 -47.72117326 77.44483
## 2004.8192 13.841905 -27.14792427 54.83173 -48.84662932 76.53044
## 2004.8219 13.244398 -27.81432090 54.30312 -49.54949401 76.03829
## 2004.8247 14.085482 -27.04201196 55.21298 -48.81359205 76.98456
## 2004.8274 15.127045 -26.06910853 56.32320 -47.87703482 78.13112
## 2004.8301 13.030070 -28.23462888 54.29477 -50.07884089 76.13898
## 2004.8329 13.924326 -27.40880484 55.25746 -49.28924240 77.13789
## 2004.8356 12.351511 -29.04993849 53.75296 -50.96654172 75.66956
## 2004.8384 13.189403 -28.28025245 54.65906 -50.23296177 76.61177
## 2004.8411 13.819218 -27.71853114 55.35697 -49.70728726 77.34572
## 2004.8438 14.453024 -27.15270750 56.05876 -49.17745143 78.08350
## 2004.8466 12.957081 -28.71652241 54.63068 -50.77719544 76.69136
## 2004.8493 11.276321 -30.46504361 53.01769 -52.56158732 75.11423
## 2004.8521 12.728505 -29.08051151 54.53752 -51.21286776 76.66988
## 2004.8548 11.828235 -30.04832354 53.70479 -52.21643448 75.87290
## 2004.8575 12.879551 -29.06444074 54.82354 -51.26824879 77.02735
## 2004.8603 12.938908 -29.07240942 54.95022 -51.31185728 77.18967
## 2004.8630 15.254812 -26.82372255 57.33335 -49.09875321 79.60838
## 2004.8658 13.756685 -28.38896017 55.90233 -50.69951687 78.21289
## 2004.8685 11.001470 -31.21117797 53.21412 -53.55720423 75.56015
## 2004.8712 11.759366 -30.52017972 54.03891 -52.90161933 76.42035
## 2004.8740 13.309972 -29.03636560 55.65631 -51.45316261 78.07311
## 2004.8767 13.619623 -28.79340121 56.03265 -51.24549994 78.48475
## 2004.8795 11.600660 -30.87894624 54.08027 -53.36629128 76.56761
## 2004.8822 11.791160 -30.75492380 54.33724 -53.27745999 76.85978
## 2004.8849 11.030053 -31.58240506 53.64251 -54.14007750 76.20018
## 2004.8877 12.956378 -29.72235026 55.63511 -52.31510430 78.22786
## 2004.8904 11.482914 -31.26198249 54.22781 -53.88976374 76.85559
## 2004.8932 12.090748 -30.72021391 54.90171 -53.38296824 77.56446
## 2004.8959 11.824955 -31.05197122 54.70188 -53.74964474 77.39955
## 2004.8986 10.653347 -32.28944124 53.59614 -55.02198031 76.32867
## 2004.9014 13.557841 -29.45070954 56.56639 -52.21806077 79.33374
## 2004.9041 12.455390 -30.61882132 55.52960 -53.42093156 78.33171
## 2004.9068 12.078343 -31.06142968 55.21812 -53.89824602 78.05493
## 2004.9096 11.930084 -31.27515063 55.13532 -54.14662042 78.00679
## 2004.9123 13.947313 -29.32328496 57.21791 -52.22935576 80.12398
## 2004.9151 13.652888 -29.68297427 56.98875 -52.62359389 79.92937
## 2004.9178 12.341342 -31.05968647 55.74237 -54.03480297 78.71749
## 2004.9205 14.066927 -29.39917008 57.53302 -52.40873174 80.54258
## 2004.9233 11.802496 -31.72857177 55.33356 -54.77252710 78.37752
## 2004.9260 11.102451 -32.49349166 54.69839 -55.57178939 77.77669
## 2004.9288 10.990515 -32.67020472 54.65124 -55.78279384 77.76382
## 2004.9315 10.633120 -33.09228204 54.35852 -56.23911174 77.50535
## 2004.9342 10.501696 -33.28829300 54.29168 -56.46931270 77.47270
## 2004.9370 12.321826 -31.53265384 56.17631 -54.74781319 79.39147
## 2004.9397 10.909636 -33.00924032 54.82851 -56.25848919 78.07776
## 2004.9425 10.954454 -33.02872500 54.93763 -56.31201348 78.22092
## 2004.9452 11.526065 -32.52132208 55.57345 -55.83860048 78.89073
## 2004.9479 9.657766 -34.45373606 53.76927 -57.80495490 77.12049
## 2004.9507 9.888240 -34.28728458 54.06376 -57.67239460 77.44887
## 2004.9534 10.834959 -33.40449466 55.07441 -56.82344682 78.49336
## 2004.9562 9.622613 -34.68067768 53.92590 -58.13342314 77.37865
## 2004.9589 10.959918 -33.40711829 55.32695 -56.89360843 78.81344
## 2004.9616 10.765645 -33.66504512 55.19633 -57.18523152 78.71652
## 2004.9644 9.846412 -34.64784043 54.34066 -58.20167489 77.89450
## 2004.9671 9.142303 -35.41542121 53.70003 -59.00285572 77.28746
## 2004.9699 8.515840 -36.10526649 53.13695 -59.72625327 76.75793
## 2004.9726 6.021963 -38.66243511 50.70636 -62.31692655 74.36085
## 2004.9753 8.058494 -36.68910601 52.80609 -60.37705473 76.49404
## 2004.9781 9.975409 -34.83530485 54.78612 -58.55666368 78.50748
## 2004.9808 10.739439 -34.13429911 55.61318 -57.88902103 79.36790
## 2004.9836 9.668891 -35.26778306 54.60556 -59.05582129 78.39360
## 2004.9863 9.141732 -35.85778986 54.14125 -59.67909781 77.96256
## 2004.9890 7.533067 -37.52921480 52.59535 -61.38374606 76.44988
## 2004.9918 9.660976 -35.46397914 54.78593 -59.35168751 78.67364
## 2004.9945 9.060576 -36.12696550 54.24812 -60.04780496 78.16896
## 2004.9973 9.798281 -35.45176029 55.04832 -59.40568502 79.00225
## 2005.0000 12.293157 -33.01929725 57.60561 -57.00626161 81.59258
## 2005.0027 12.709784 -32.66499814 58.08457 -56.68495669 82.10452
## 2005.0055 11.400790 -34.03623354 56.83781 -58.08914101 80.89072
## 2005.0082 11.100237 -34.39894340 56.59942 -58.48475473 80.68523
## 2005.0110 10.869974 -34.69127824 56.43123 -58.80994854 80.54990
## 2005.0137 12.370131 -33.25310918 57.99337 -57.40459374 82.14486
## 2005.0164 12.962118 -32.72302548 58.64726 -56.90727977 82.83152
## 2005.0192 10.732447 -35.01451683 56.47941 -59.23149651 80.69639
## 2005.0219 10.696135 -35.11256503 56.50483 -59.36222594 80.75450
## 2005.0247 10.808086 -35.06226747 56.67844 -59.34456562 80.96074
## 2005.0274 13.228469 -32.70345427 59.16039 -57.01834586 83.47528
## 2005.0301 12.859264 -33.13414810 58.85268 -57.48158949 83.20012
## 2005.0329 12.738680 -33.31613803 58.79350 -57.69608577 83.17344
## 2005.0356 11.767162 -34.34898019 57.88330 -58.76139099 82.29571
## 2005.0384 12.672229 -33.50515584 58.84961 -57.94998659 83.29444
## 2005.0411 12.935372 -33.30317441 59.17392 -57.78038218 83.65113
## 2005.0438 14.177364 -32.12226295 60.47699 -56.63180495 84.98653
## 2005.0466 10.797635 -35.56299216 57.15826 -60.10482580 81.70010
## 2005.0493 11.810703 -34.61084491 58.23225 -59.18492776 82.80633
## 2005.0521 12.395595 -34.08679263 58.87798 -58.69308242 83.48427
## 2005.0548 11.255144 -35.28800449 57.79829 -59.92645912 82.43675
## 2005.0575 11.820608 -34.78322251 58.42444 -59.45380005 83.09502
## 2005.0603 10.189616 -36.47481750 56.85405 -61.17747617 81.55671
## 2005.0630 9.907523 -36.81743431 56.63248 -61.55213250 81.36718
## 2005.0658 12.506252 -34.27915054 59.29166 -59.04584681 84.05835
## 2005.0685 11.231639 -35.61413190 58.07741 -60.41278496 82.87606
## 2005.0712 9.151921 -37.75414035 56.05798 -62.58470907 80.88855
## 2005.0740 12.895457 -34.07081617 59.86173 -58.93325958 84.72417
## 2005.0767 13.498790 -33.52761896 60.52520 -58.42189625 85.41948
## 2005.0795 12.977617 -34.10885073 60.06409 -59.03492124 84.99016
## 2005.0822 13.081694 -34.06475613 60.22814 -59.02257936 85.18597
## 2005.0849 13.364708 -33.84164841 60.57106 -58.83118402 85.56060
## 2005.0877 12.422666 -34.84352068 59.68885 -59.86472846 84.71006
## 2005.0904 14.367918 -32.95802271 61.69386 -58.01086264 86.74670
## 2005.0932 13.545399 -33.84022121 60.93102 -58.92465339 86.01545
## 2005.0959 12.674579 -34.77064571 60.11980 -59.88663041 85.23579
## 2005.0986 12.870449 -34.63430506 60.37520 -59.78180268 85.52270
## 2005.1014 12.596089 -34.96811935 60.16030 -60.14709046 85.33927
## 2005.1041 11.758253 -35.86533603 59.38184 -61.07574133 84.59225
## 2005.1068 12.536246 -35.14664986 60.21914 -60.38845021 85.46094
## 2005.1096 12.058714 -35.68341472 59.80084 -60.95657112 85.07400
## 2005.1123 10.818531 -36.98275732 58.61982 -62.28723090 83.92429
## 2005.1151 13.143482 -34.71689313 61.00386 -60.05264519 86.33961
## 2005.1178 14.085787 -33.83360132 62.00518 -59.20059330 87.37217
## 2005.1205 13.683871 -34.29445829 61.66220 -59.69265176 87.06039
## 2005.1233 11.651619 -36.38557901 59.68882 -61.81493569 85.11817
## 2005.1260 11.477994 -36.61800086 59.57399 -62.07848259 85.03447
## 2005.1288 11.616076 -36.53864376 59.77080 -62.03021256 85.26236
## 2005.1315 13.957130 -34.25624340 62.17050 -59.77886139 87.69312
## 2005.1342 13.114389 -35.15756612 61.38634 -60.71119558 86.93997
## 2005.1370 10.389784 -37.94068170 58.72025 -63.52528503 84.30485
## 2005.1397 11.101115 -37.28779179 59.49002 -62.90333155 85.10556
## 2005.1425 12.268456 -36.17882010 60.71573 -61.82525897 86.36217
## 2005.1452 12.414861 -36.09071478 60.92044 -61.76801557 86.59774
## 2005.1479 13.675931 -34.88787426 62.23974 -60.59599993 87.94786
## 2005.1507 14.597821 -34.02414398 63.21979 -59.76305760 88.95870
## 2005.1534 13.834977 -34.84507896 62.51503 -60.61474376 88.28470
## 2005.1562 13.069035 -35.66904216 61.80711 -61.46942149 87.60749
## 2005.1589 11.800443 -36.99558575 60.59647 -62.82664308 86.42753
## 2005.1616 12.848860 -36.00505191 61.70277 -61.86675086 87.56447
## 2005.1644 12.930553 -35.98117450 61.84228 -61.87347879 87.73458
## 2005.1671 13.077464 -35.89200978 62.04694 -61.81488329 87.96981
## 2005.1699 14.620315 -34.40683685 63.64747 -60.36024356 89.60087
## 2005.1726 14.692896 -34.39186732 63.77766 -60.37577137 89.76156
## 2005.1753 14.270794 -34.87151243 63.41310 -60.88587806 89.42747
## 2005.1781 14.738626 -34.46115691 63.93841 -60.50594849 89.98320
## 2005.1808 11.857418 -37.39977327 61.11461 -63.47495529 87.18979
## 2005.1836 9.091919 -40.22261447 58.40645 -66.32815156 84.51199
## 2005.1863 9.914159 -39.45764963 59.28597 -65.59350653 85.42183
## 2005.1890 12.880308 -36.54871036 62.30933 -62.71485196 88.47547
## 2005.1918 13.535456 -35.95070468 63.02162 -62.14709594 89.21801
## 2005.1945 13.569903 -35.97333480 63.11314 -62.19994085 89.33975
## 2005.1973 13.771620 -35.82862988 63.37187 -62.08541593 89.62866
## 2005.2000 14.258552 -35.39864326 63.91575 -61.68557467 90.20268
## 2005.2027 14.964083 -34.74999301 64.67816 -61.06703526 90.99520
## 2005.2055 17.118255 -32.65263701 66.88915 -58.99975567 93.23627
## 2005.2082 16.635054 -33.19258918 66.46270 -59.56974997 92.83986
## 2005.2110 14.657036 -35.22729316 64.54137 -61.63446189 90.94853
## 2005.2137 13.368753 -36.57219779 63.30970 -63.00934041 89.74685
## 2005.2164 14.992072 -35.00543747 64.98958 -61.47252004 91.45666
## 2005.2192 15.548627 -34.50537610 65.60263 -61.00236478 92.09962
## 2005.2219 14.688821 -35.42161230 64.79925 -61.94847337 91.32612
## 2005.2247 13.925324 -36.24147607 64.09212 -62.79817593 90.64882
## 2005.2274 15.691895 -34.53120910 65.91500 -61.11771426 92.50150
## 2005.2301 16.003726 -34.27561849 66.28307 -60.89189558 92.89935
## 2005.2329 17.353855 -32.98166713 67.68938 -59.62768289 94.33539
## 2005.2356 16.781209 -33.61042837 67.17285 -60.28614964 93.84857
## 2005.2384 18.005325 -32.44236434 68.45301 -59.14775807 95.15841
## 2005.2411 17.256063 -33.24761753 67.75974 -59.98265080 94.49478
## 2005.2438 17.343729 -33.21587974 67.90334 -59.98051971 94.66798
## 2005.2466 16.668762 -33.94671330 67.28424 -60.74092728 94.07845
## 2005.2493 16.824957 -33.84632275 67.49624 -60.67007812 94.31999
## 2005.2521 18.180715 -32.54630872 68.90774 -59.39957298 95.76100
## 2005.2548 18.298618 -32.48408808 69.08132 -59.36682884 95.96406
## 2005.2575 17.518525 -33.31980295 68.35685 -60.23198792 95.26904
## 2005.2603 17.012144 -33.88174381 67.90603 -60.82334082 94.84763
## 2005.2630 17.713327 -33.23606111 68.66272 -60.20703808 95.63369
## 2005.2658 18.915166 -32.08966241 69.91999 -59.08998737 96.92032
## 2005.2685 17.588966 -33.47124126 68.64917 -60.50088235 95.67881
## 2005.2712 17.762945 -33.35258181 68.87847 -60.41150727 95.93740
## 2005.2740 17.878965 -33.29182125 69.04975 -60.37999941 96.13793
## 2005.2767 16.172771 -35.05321615 67.39876 -62.17061547 94.51616
## 2005.2795 15.560278 -35.72084890 66.84141 -62.86743791 93.98799
## 2005.2822 16.136639 -35.19956930 67.47285 -62.37531665 94.64860
## 2005.2849 16.661509 -34.72972206 68.05274 -61.93459651 95.25761
## 2005.2877 18.613103 -32.83309194 70.05930 -60.06706233 97.29327
## 2005.2904 19.773956 -31.72714402 71.27506 -58.99017930 98.53809
## 2005.2932 20.181792 -31.37415396 71.73774 -58.66622317 99.02981
## 2005.2959 20.157741 -31.45299303 71.76848 -58.77406532 99.08955
## 2005.2986 19.572442 -32.09302209 71.23791 -59.44306671 98.58795
## 2005.3014 18.427225 -33.29291077 70.14736 -60.67189705 97.52635
## 2005.3041 17.703779 -34.07097184 69.47853 -61.47886923 96.88643
## 2005.3068 18.020680 -33.80862698 69.84999 -61.24540501 97.28677
## 2005.3096 18.990083 -32.89372371 70.87389 -60.35935201 98.33952
## 2005.3123 18.675156 -33.26309289 70.61341 -60.75754120 98.10785
## 2005.3151 17.776550 -34.21608452 69.76918 -61.73932264 97.29242
## 2005.3178 17.508823 -34.53814009 69.55579 -62.09013795 97.10778
## 2005.3205 18.143298 -33.95793618 70.24453 -61.53866379 97.82526
## 2005.3233 18.356111 -33.79933915 70.51156 -61.40876661 98.12099
## 2005.3260 19.101355 -33.10825396 71.31096 -60.74635148 98.94906
## 2005.3288 18.540640 -33.72307149 70.80435 -61.38980934 98.47109
## 2005.3315 17.696061 -34.62169795 70.01382 -62.31704653 97.70917
## 2005.3342 17.992708 -34.37904162 70.36446 -62.10297139 98.08839
## 2005.3370 18.195672 -34.23001390 70.62136 -61.98249544 98.37384
## 2005.3397 20.025059 -32.45450710 72.50462 -60.23551107 100.28563
## 2005.3425 19.337963 -33.19542738 71.87135 -61.00492451 99.68085
## 2005.3452 18.636581 -33.95057937 71.22374 -61.78854050 99.06170
## 2005.3479 18.584852 -34.05602326 71.22573 -61.92241932 99.09212
## 2005.3507 19.183317 -33.51121809 71.87785 -61.40602009 99.77265
## 2005.3534 19.874027 -32.87411364 72.62217 -60.79729269 100.54535
## 2005.3562 19.796560 -33.00513221 72.59825 -60.95665949 100.54978
## 2005.3589 20.773392 -32.08179634 73.62858 -60.06164314 101.60843
## 2005.3616 20.159768 -32.74886387 73.06840 -60.75700155 101.07654
## 2005.3644 19.932499 -33.02952166 72.89452 -61.06592167 100.93092
## 2005.3671 20.076747 -32.93860885 73.09210 -61.00324273 101.15674
## 2005.3699 20.039185 -33.02945200 73.10782 -61.12229138 101.20066
## 2005.3726 20.056469 -33.06539550 73.17833 -61.18641208 101.29935
## 2005.3753 19.692924 -33.48211585 72.86796 -61.63128143 101.01713
## 2005.3781 19.807539 -33.42062214 73.03570 -61.59790860 101.21299
## 2005.3808 19.863035 -33.41819499 73.14426 -61.62357430 101.34964
## 2005.3836 21.277769 -32.05647640 74.61201 -60.28992060 102.84546
## 2005.3863 20.926291 -32.46091778 74.31350 -60.72239899 102.57498
## 2005.3890 21.059098 -32.38102108 74.49922 -60.67051152 102.78871
## 2005.3918 20.245526 -33.24745238 73.73850 -61.56492435 102.05598
## 2005.3945 19.612115 -33.93366862 73.15790 -62.27909450 101.50333
## 2005.3973 19.601465 -33.99707313 73.20000 -62.37042538 101.57336
## 2005.4000 19.975418 -33.67582210 73.62666 -62.07707326 102.02791
## 2005.4027 20.105230 -33.59866154 73.80912 -62.02778423 102.23824
## 2005.4055 20.201167 -33.55532297 73.95766 -62.01228989 102.41462
## 2005.4082 19.319197 -34.48984047 73.12823 -62.97462440 101.61302
## 2005.4110 20.635953 -33.22558126 74.49749 -61.73815506 103.01006
## 2005.4137 21.255782 -32.65819701 75.16976 -61.19853362 103.71010
## 2005.4164 21.229521 -32.73685207 75.19589 -61.30492452 103.76397
## 2005.4192 20.195248 -33.82346889 74.21396 -62.41925027 102.80975
## 2005.4219 20.377302 -33.69370774 74.44831 -62.31717123 103.07178
## 2005.4247 19.712661 -34.41059103 73.83591 -63.06170988 102.48703
## 2005.4274 19.661051 -34.51439315 73.83649 -63.19314070 102.51524
## 2005.4301 19.672858 -34.55472779 73.90044 -63.26107744 102.60679
## 2005.4329 19.799030 -34.48064725 74.07871 -63.21457249 102.81263
## 2005.4356 19.876861 -34.45485708 74.20858 -63.21633147 102.97005
## 2005.4384 20.734980 -33.64873047 75.11869 -62.43772765 103.90769
## 2005.4411 19.923246 -34.51240647 74.35890 -63.32890015 103.17539
## 2005.4438 19.890735 -34.59680954 74.37828 -63.44077350 103.22224
## 2005.4466 19.385694 -35.15369455 73.92508 -64.02510266 102.79649
## 2005.4493 19.706667 -34.88451480 74.29785 -63.78334100 103.19668
## 2005.4521 20.251052 -34.39187537 74.89398 -63.31809368 103.82020
## 2005.4548 20.365241 -34.32938189 75.05986 -63.28296638 104.01345
## 2005.4575 20.837822 -33.90844835 75.58409 -62.88937318 104.56502
## 2005.4603 20.355115 -34.44275390 75.15298 -63.45099330 104.16122
## 2005.4630 20.791813 -34.05760598 75.64123 -63.09313426 104.67676
## 2005.4658 21.191192 -33.70972765 76.09211 -62.77251919 105.15490
## 2005.4685 20.481799 -34.47057466 75.43417 -63.56060391 104.52420
## 2005.4712 20.739408 -34.26437023 75.74319 -63.38161170 104.86043
## 2005.4740 20.814072 -34.24106318 75.86921 -63.38549147 105.01364
## 2005.4767 21.115366 -33.99107848 76.22181 -63.16266825 105.39340
## 2005.4795 21.293893 -33.86381349 76.45160 -63.06253947 105.65033
## 2005.4822 21.384012 -33.82490855 76.59293 -63.05074555 105.81877
## 2005.4849 21.441909 -33.81817805 76.70200 -63.07110094 105.95492
## 2005.4877 21.297473 -34.01373263 76.60868 -63.29371636 105.88866
## 2005.4904 22.076523 -33.28575438 77.43880 -62.59277396 106.74582
## 2005.4932 22.195206 -33.21809651 77.60851 -62.55212702 106.94254
## 2005.4959 22.309310 -33.15497048 77.77359 -62.51598707 107.13461
## 2005.4986 22.291116 -33.22409549 77.80633 -62.61207338 107.19431
## 2005.5014 21.755836 -33.81026016 77.32193 -63.22517464 106.73685
## 2005.5041 22.035171 -33.58176298 77.65211 -63.02358940 107.09393
## 2005.5068 22.290169 -33.37755644 77.95789 -62.84627023 107.42661
## 2005.5096 21.530987 -34.18748317 77.24946 -63.68305982 106.74503
## 2005.5123 21.893317 -33.87585282 77.66249 -63.39826789 107.18490
## 2005.5151 22.143876 -33.67594685 77.96370 -63.22517596 107.51293
## 2005.5178 22.394683 -33.47574691 78.26511 -63.05176574 107.84113
## 2005.5205 22.093827 -33.82716325 78.01482 -63.42994757 107.61760
## 2005.5233 21.849357 -34.12214955 77.82086 -63.75167517 107.45039
## 2005.5260 21.190832 -34.83114447 77.21281 -64.48738729 106.86905
## 2005.5288 20.514867 -35.55753374 76.58727 -65.24046971 106.27020
## 2005.5315 21.043148 -35.07963174 77.16593 -64.78923687 106.87553
## 2005.5342 21.377299 -34.79581549 77.55041 -64.53206586 107.28666
## 2005.5370 21.305491 -34.91791208 77.52889 -64.68078385 107.29177
## 2005.5397 21.713465 -34.56018258 77.98711 -64.34965195 107.77658
## 2005.5425 22.009961 -34.31388524 78.33381 -64.12992848 108.14985
## 2005.5452 22.017628 -34.35637342 78.39163 -64.19896687 108.23422
## 2005.5479 21.492663 -34.93144829 77.91677 -64.80056835 107.78589
## 2005.5507 21.237449 -35.23672758 77.71163 -65.13235071 107.60725
## 2005.5534 20.897338 -35.62685928 77.42154 -65.54896201 107.34364
## 2005.5562 20.733311 -35.84086300 77.30749 -65.78942192 107.25604
## 2005.5589 21.173944 -35.45016286 77.79805 -65.42515461 107.77304
## 2005.5616 21.287553 -35.38644264 77.96155 -65.38784394 107.96295
## 2005.5644 21.741634 -34.98220727 78.46547 -65.00999489 108.49326
## 2005.5671 21.576427 -35.19721530 78.35007 -65.25136607 108.40422
## 2005.5699 21.894851 -34.92854863 78.71825 -65.00903946 108.79874
## 2005.5726 22.251280 -34.62183395 79.12439 -64.72864178 109.23120
## 2005.5753 21.906217 -35.01656735 78.82900 -65.14966920 108.96210
## 2005.5781 22.115503 -34.85690903 79.08791 -65.01628198 109.24729
## 2005.5808 22.023979 -34.99801673 79.04597 -65.18363790 109.23160
## 2005.5836 21.237686 -35.83385078 78.30922 -66.04569738 108.52107
## 2005.5863 21.576145 -35.54488999 78.69718 -65.78293927 108.93523
## 2005.5890 21.734275 -35.43621532 78.90476 -65.70044460 109.16899
## 2005.5918 22.001135 -35.21876787 79.22104 -65.50915452 109.51142
## 2005.5945 22.533583 -34.73568879 79.80286 -65.05221023 110.11938
## 2005.5973 22.749353 -34.56924665 80.06795 -64.91188039 110.41059
## 2005.6000 22.675904 -34.69198079 80.04379 -65.06070436 110.41251
## 2005.6027 22.027887 -35.38923996 79.44501 -65.78403097 109.83981
## 2005.6055 21.382274 -36.08405302 78.84860 -66.50488913 109.26944
## 2005.6082 20.633116 -36.88236970 78.14860 -67.32922864 108.59546
## 2005.6110 20.723915 -36.84068708 78.28852 -67.31354662 108.76138
## 2005.6137 21.165930 -36.44774645 78.77961 -66.94658442 109.27844
## 2005.6164 21.682840 -35.97986890 79.34555 -66.50466321 109.87034
## 2005.6192 21.741977 -35.96972310 79.45368 -66.52045168 110.00441
## 2005.6219 21.318824 -36.44182540 79.07947 -67.01846625 109.65611
## 2005.6247 20.329233 -37.48032405 78.13879 -68.08285525 108.74132
## 2005.6274 20.936372 -36.92205211 78.79480 -67.55045175 109.42320
## 2005.6301 21.981265 -35.92598460 79.88851 -66.58023087 110.54276
## 2005.6329 21.332651 -36.62338292 79.28868 -67.30345403 109.96876
## 2005.6356 21.078848 -36.92592871 79.08363 -67.63180296 109.78950
## 2005.6384 21.788416 -36.26506328 79.84190 -66.99671899 110.57355
## 2005.6411 21.821701 -36.28044031 79.92384 -67.03785586 110.68126
## 2005.6438 22.258517 -35.89224438 80.40928 -66.67539824 111.19243
## 2005.6466 22.189811 -36.00953132 80.38915 -66.81840196 111.19802
## 2005.6493 20.742659 -37.50522233 78.99054 -68.33978832 109.82511
## 2005.6521 20.844853 -37.45152756 79.14123 -68.31176750 110.00147
## 2005.6548 20.018382 -38.32645748 78.36322 -69.21235003 109.24911
## 2005.6575 20.533995 -37.85926359 78.92725 -68.77078746 109.83878
## 2005.6603 20.374670 -38.06696690 78.81631 -69.00410086 109.75344
## 2005.6630 20.189322 -38.30065400 78.67930 -69.26337686 109.64202
## 2005.6658 20.513849 -38.02442496 79.05212 -69.01271559 110.04041
## 2005.6685 20.345192 -38.24134142 78.93173 -69.25517875 109.94556
## 2005.6712 20.241127 -38.39362589 78.87588 -69.43298888 109.91524
## 2005.6740 19.755335 -38.92759654 78.43827 -69.99246423 109.50314
## 2005.6767 19.049696 -39.68137579 77.78077 -70.77172725 108.87112
## 2005.6795 19.229316 -39.54985668 78.00849 -70.66567104 109.12430
## 2005.6822 19.543842 -39.28339202 78.37108 -70.42464846 109.51233
## 2005.6849 19.571459 -39.30379676 78.44671 -70.47047451 109.61339
## 2005.6877 20.324329 -38.59890918 79.24757 -69.79098752 110.43965
## 2005.6904 18.867605 -40.10357782 77.83879 -71.32103608 109.05625
## 2005.6932 18.504384 -40.51470374 77.52347 -71.75752131 108.76629
## 2005.6959 19.234976 -39.83197702 78.30193 -71.10013333 109.57009
## 2005.6986 18.807392 -40.30738809 77.92217 -71.60086262 109.21565
## 2005.7014 18.841404 -40.32116556 78.00397 -71.63993785 109.32275
## 2005.7041 18.730012 -40.48030704 77.94033 -71.82435667 109.28438
## 2005.7068 18.593233 -40.66479793 77.85126 -72.03410453 109.22057
## 2005.7096 18.306417 -40.99928737 77.61212 -72.39383062 109.00666
## 2005.7123 17.458791 -41.89454745 76.81213 -73.31430708 108.23189
## 2005.7151 17.859130 -41.54180552 77.26007 -72.98676131 108.70502
## 2005.7178 18.141785 -41.30670918 77.59028 -72.77684095 109.06041
## 2005.7205 18.711876 -40.78413818 78.20789 -72.27942582 109.70318
## 2005.7233 18.225893 -41.31760390 77.76939 -72.83802732 109.28981
## 2005.7260 18.708023 -40.88291861 78.29897 -72.42845779 109.84450
## 2005.7288 18.945196 -40.69315282 78.58355 -72.26378777 110.15418
## 2005.7315 17.768960 -41.91675876 77.45468 -73.51246956 109.05039
## 2005.7342 17.730998 -42.00205233 77.46405 -73.62281908 109.08482
## 2005.7370 16.791329 -42.98901577 76.57167 -74.63481864 108.21748
## 2005.7397 16.936226 -42.89137541 76.76383 -74.56219461 108.43465
## 2005.7425 17.482168 -42.39265336 77.35699 -74.08846915 109.05280
## 2005.7452 18.189207 -41.73279646 78.11121 -73.45358913 109.83200
## 2005.7479 18.542392 -41.42675684 78.51154 -73.17250674 110.25729
## 2005.7507 17.627484 -42.38877308 77.64374 -74.15946061 109.41443
## 2005.7534 18.368852 -41.69447704 78.43218 -73.49008264 110.22779
## 2005.7562 16.596880 -43.51348337 76.70724 -75.33398754 108.52775
## 2005.7589 16.818755 -43.33860606 76.97612 -75.18398931 108.82150
## 2005.7616 16.522339 -43.68198264 76.72666 -75.55222557 108.59690
## 2005.7644 15.761034 -44.49021200 76.01228 -76.38529522 107.90736
## 2005.7671 16.854606 -43.44352872 77.15274 -75.36343290 109.07264
## 2005.7699 17.076627 -43.26835915 77.42161 -75.21306501 109.36632
## 2005.7726 16.584224 -43.80757719 76.97602 -75.77706548 108.94551
## 2005.7753 17.224579 -43.21400106 77.66316 -75.20825259 109.65741
## 2005.7781 17.092659 -43.39266391 77.57798 -75.41165953 109.59698
## 2005.7808 17.089652 -43.44237686 77.62168 -75.48609745 109.66540
## 2005.7836 17.660591 -42.91810841 78.23929 -74.98653492 110.30772
## 2005.7863 16.821719 -43.80361552 77.44705 -75.89672893 109.54017
## 2005.7890 16.114327 -44.55760570 76.78626 -76.67538704 108.90404
## 2005.7918 15.553872 -45.16462424 76.27237 -77.30705457 108.41480
## 2005.7945 16.219957 -44.54506683 76.98498 -76.71212726 109.15204
## 2005.7973 16.052219 -44.75929618 76.86373 -76.95096786 109.05541
## 2005.8000 15.216095 -45.64187619 76.07407 -77.85814034 108.29033
## 2005.8027 15.823018 -45.08137453 76.72741 -77.32221237 108.96825
## 2005.8055 16.069497 -44.88128120 77.02027 -77.14667402 109.28567
## 2005.8082 15.829887 -45.16724152 76.82701 -77.45717065 109.11694
## 2005.8110 15.771403 -45.27203969 76.81485 -77.58648650 109.12929
## 2005.8137 15.144422 -45.94530066 76.23415 -78.28424657 108.57309
## 2005.8164 14.861826 -46.27414173 75.99779 -78.63756817 108.36122
## 2005.8192 13.841905 -47.34027245 75.02408 -79.72816093 107.41197
## 2005.8219 13.244398 -47.98395428 74.47275 -80.39628635 106.88508
## 2005.8247 14.085482 -47.18901115 75.35997 -79.62576838 107.79673
## 2005.8274 15.127045 -46.19355363 76.44764 -78.65471764 108.90881
## 2005.8301 13.030070 -48.33659949 74.39674 -80.82215194 106.88229
## 2005.8329 13.924326 -47.48838006 75.33703 -79.99830267 107.84695
## 2005.8356 12.351511 -49.10719695 73.81022 -81.64147145 106.34449
## 2005.8384 13.189403 -48.31527230 74.69408 -80.87388048 107.25269
## 2005.8411 13.819218 -47.73139004 75.36983 -80.31431373 107.95275
## 2005.8438 14.453024 -47.14348265 76.04953 -79.75070371 108.65675
## 2005.8466 12.957081 -48.68529053 74.59945 -81.31679087 107.23095
## 2005.8493 11.276321 -50.41188097 72.96452 -83.06764254 105.62028
## 2005.8521 12.728505 -49.00549390 74.46250 -81.68549869 107.14251
## 2005.8548 11.828235 -49.95152630 73.60800 -82.65575634 106.31223
## 2005.8575 12.879551 -48.94593875 74.70504 -81.67437611 107.43348
## 2005.8603 12.938908 -48.93227714 74.81009 -81.68490392 107.56272
## 2005.8630 15.254812 -46.66203397 77.17166 -79.43883233 109.94846
## 2005.8658 13.756685 -48.20578885 75.71916 -81.00674097 108.52011
## 2005.8685 11.001470 -51.00659702 73.00954 -83.83168513 105.83463
## 2005.8712 11.759366 -50.29426183 73.81299 -83.14346819 106.66220
## 2005.8740 13.309972 -48.78918302 75.40913 -81.66248995 108.28243
## 2005.8767 13.619623 -48.52502577 75.76427 -81.42241560 108.66166
## 2005.8795 11.600660 -50.58944936 73.79077 -83.51090448 106.71222
## 2005.8822 11.791160 -50.44437646 74.02670 -83.38987929 106.97220
## 2005.8849 11.030053 -51.25087784 73.31098 -84.22041083 106.28052
## 2005.8877 12.956378 -49.36991332 75.28267 -82.36345898 108.27622
## 2005.8904 11.482914 -50.88870558 73.85453 -83.90624643 106.87207
## 2005.8932 12.090748 -50.32616638 74.50766 -83.36768501 107.54918
## 2005.8959 11.824955 -50.63722202 74.28713 -83.70270105 107.35261
## 2005.8986 10.653347 -51.85405893 73.16075 -84.94348099 106.25018
## 2005.9014 13.557841 -48.99476228 76.11044 -82.10811007 109.22379
## 2005.9041 12.455390 -50.14237686 75.05316 -83.27963310 108.19041
## 2005.9068 12.078343 -50.56455540 74.72124 -83.72570286 107.88239
## 2005.9096 11.930084 -50.75791354 74.61808 -83.94293501 107.80310
## 2005.9123 13.947313 -48.78575165 76.68038 -81.99462997 109.88926
## 2005.9151 13.652888 -49.12521098 76.43099 -82.35792903 109.66370
## 2005.9178 12.341342 -50.48175907 75.16444 -83.73829975 108.42098
## 2005.9205 14.066927 -48.80114405 76.93500 -82.08149032 110.21534
## 2005.9233 11.802496 -51.11051223 74.71550 -84.41464706 108.01964
## 2005.9260 11.102451 -51.85546336 74.06036 -85.18336977 107.38827
## 2005.9288 10.990515 -52.01227205 73.99330 -85.36393311 107.34496
## 2005.9315 10.633120 -52.41450902 73.68075 -85.78990782 107.05615
## 2005.9342 10.501696 -52.59074330 73.59413 -85.98986297 106.99325
## 2005.9370 12.321826 -50.81539079 75.45904 -84.23821448 108.88187
## 2005.9397 10.909636 -52.27232688 74.09160 -85.71883780 107.53811
## 2005.9425 10.954454 -52.27222378 74.18113 -85.74240518 107.65131
## 2005.9452 11.526065 -51.74529536 74.79743 -85.23913049 108.29126
## 2005.9479 9.657766 -53.65824576 72.97378 -87.17571794 106.49125
## 2005.9507 9.888240 -53.47239229 73.24887 -87.01348486 106.78996
## 2005.9534 10.834959 -52.57026164 74.24018 -86.13495797 107.80488
## 2005.9562 9.622613 -53.82716484 73.07239 -87.41544835 106.66067
## 2005.9589 10.959918 -52.53438621 74.45422 -86.14624035 108.06608
## 2005.9616 10.765645 -52.77315405 74.30444 -86.40856230 107.93985
## 2005.9644 9.846412 -53.73685030 73.42967 -87.39579618 107.08862
## 2005.9671 9.142303 -54.48539162 72.77000 -88.16785868 106.45247
## 2005.9699 8.515840 -55.15625673 72.18794 -88.86222854 105.89391
## 2005.9726 6.021963 -57.69450412 69.73843 -91.42396433 103.46789
## 2005.9753 8.058494 -55.70231245 71.81930 -89.45524469 105.57223
## 2005.9781 9.975409 -53.82970706 73.78052 -87.60609503 107.55691
## 2005.9808 10.739439 -53.10995508 74.58883 -86.90978250 108.38866
## 2005.9836 9.668891 -54.22475052 73.56253 -88.04800114 107.38578
## 2005.9863 9.141732 -54.79612620 73.07959 -88.64278383 106.92625
## 2005.9890 7.533067 -56.44897712 71.51511 -90.31902557 105.38516
## 2005.9918 9.660976 -54.36522424 73.68718 -88.25864736 107.58060
## 2005.9945 9.060576 -55.00974986 73.13090 -88.92653156 107.04768
## 2005.9973 9.798281 -54.31614011 73.91270 -88.25626430 107.85283
## 2006.0000 12.293157 -51.86532844 76.45164 -85.82877907 110.41509
## 2006.0027 12.709784 -51.49273629 76.91230 -85.47949737 110.89906
## 2006.0055 11.400790 -52.84573398 75.64731 -86.85578952 109.65737##NOTE: AIC = 20079.90 , BIC = 20096.98 , RMSE = 2.075702 Also, the headline of the plot below contains ETS(A,N,N) showing that the automated model characterized error of the “tsWSR_PK” SERIES as Additative (A), trend as None (A) and seasonality as None (N) which is equivalent to simple exponential model(ses) with only alpha parameter i.e level.
#Model 2 : ARIMA Models(AutoRegressive Moving Average) It is used for forecasting for both seasonal and non- seasonal level.
#Changing to stationary set
train.sta_Var4 <- diff(train3)
test.sta_Var4 <- diff(test3)#2.1 Auto Arima model without sesonality:
set.seed(301)
model_Var4 <- auto.arima(train.sta_Var4, seasonal = FALSE)
summary(model_Var4)## Series: train.sta_Var4
## ARIMA(1,0,3) with zero mean
##
## Coefficients:
## ar1 ma1 ma2 ma3
## 0.3077 -0.5011 -0.2231 -0.0916
## s.e. 0.1082 0.1092 0.0350 0.0490
##
## sigma^2 estimated as 4.805: log likelihood=-4829
## AIC=9667.99 AICc=9668.02 BIC=9696.46
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 0.001500922 2.19006 1.494088 NaN Inf 0.6431976 -0.0005031034##NOTE: AIC = 9667.99 , BIC = 9696.46 , RMSE = 2.19006
tsdisplay(residuals(model_Var4), lag.max = 45, main = '(1,1,1) Model Residuals')
#2.2 Auto Arima model with sesonality:
set.seed(301)
model2_Var4 <- auto.arima(train.sta_Var4, seasonal= TRUE)
summary(model2_Var4)## Series: train.sta_Var4
## ARIMA(2,0,1) with zero mean
##
## Coefficients:
## ar1 ar2 ma1
## 0.6801 -0.1497 -0.8753
## s.e. 0.0273 0.0234 0.0190
##
## sigma^2 estimated as 4.806: log likelihood=-4829.78
## AIC=9667.55 AICc=9667.57 BIC=9690.32
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 0.001505874 2.190842 1.493964 NaN Inf 0.6431441 0.001093764##NOTE: AIC =9667.55, BIC = 9690.32, RMSE = 2.190842
tsdisplay(residuals(model2_Var4), lag.max = 20, main = 'Seasonal Model Residuals')
NOTE: Above Graphs shows serious lags at 15
#2.3 Manual Arima Passing parameter order = (2,0,15) which means p(member of lags of a variable to be used as a predictor) = 2, d = 0(members of differences needed for stationarity) and q = 15 (moving average order - number of lagged forecasts error in the prediction equation)
set.seed(301)
model1_Var4 <- arima(train.sta_Var4, order = c(2,0,15))
summary(model1_Var4)##
## Call:
## arima(x = train.sta_Var4, order = c(2, 0, 15))
##
## Coefficients:
## ar1 ar2 ma1 ma2 ma3 ma4 ma5 ma6
## -0.2732 0.2377 0.0767 -0.5772 -0.2038 -0.0118 0.0182 -0.0164
## s.e. 0.2844 0.2034 0.2843 0.2003 0.1017 0.0859 0.0451 0.0262
## ma7 ma8 ma9 ma10 ma11 ma12 ma13 ma14
## -0.0165 -0.0034 0.0141 0.0129 0.0165 0.0359 -0.0240 -0.0297
## s.e. 0.0257 0.0268 0.0247 0.0259 0.0258 0.0258 0.0274 0.0263
## ma15 intercept
## -0.0450 0.0003
## s.e. 0.0257 0.0112
##
## sigma^2 estimated as 4.763: log likelihood = -4821.44, aic = 9680.88
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 0.0006981842 2.182491 1.489708 NaN Inf 0.6420169 0.0001722461##NOTE: AIC = 9680.88 , RMSE = 2.182491
tsdisplay(residuals(model1_Var4), lag.max = 20, main = 'Seasonal Model Residuals')
Note: It seems good fit.
Fit the observed with the predicted values for both models in the same plot.
#Plotting forecast for each model
par(mfrow = c(2,2))
fit_auto_train_Var4 %>% forecast(h=341) %>% autoplot() 
model1_Var4 %>% forecast(h=341) %>% autoplot() 
model2_Var4 %>% forecast(h=341) %>% autoplot() 
model_Var4 %>% forecast(h=341) %>% autoplot() 
Plot and comment on the residuals of the fitted data for both models in the same plot.
Residual Plot - to confirm no problem with this model
par(mfrow= c(2,2))
hist(fit_auto_train_Var4$residuals,col = 'red',xlab = 'Error',main = 'Histogram Of Residuals',freq= FALSE)
lines(density(fit_auto_train_Var4$residuals))
hist(model_Var4$residuals,col = 'red',xlab = 'Error',main = 'Histogram Of Residuals',freq= FALSE)
lines(density(model_Var4$residuals))
hist(model1_Var4$residuals,col = 'red',xlab = 'Error',main = 'Histogram Of Residuals',freq= FALSE)
lines(density(model1_Var4$residuals))
hist(model2_Var4$residuals,col = 'red',xlab = 'Error',main = 'Histogram Of Residuals',freq= FALSE)
lines(density(model2_Var4$residuals))
OBSERVATION: The residuals for each model are normally distributed, which shows the good fit of the models. It is normally distributed
Testing the autocorrelation and partial autocorrelation of the residuals (using the plots and Ljung-Box Q statistic) up to an appropriate lag *
- ACF & PACF Plots
par(mfrow = c(4,2))
acf(fit_auto_train_Var4$residuals, main = 'Correlogram')
pacf(fit_auto_train_Var4$residuals, main = 'Partial Corelogram')
acf(model_Var4$residuals, main = 'Correlogram')
pacf(model_Var4$residuals, main = 'Partial Corelogram')
acf(model1_Var4$residuals, main = 'Correlogram')
pacf(model1_Var4$residuals, main = 'Partial Corelogram')
acf(model2_Var4$residuals, main = 'Correlogram')
pacf(model2_Var4$residuals, main = 'Partial Corelogram')
NOTE:
1. Residuals are the difference between actaual and fitted values
2. These blue lines are signficance bounds
3. This graph shows us the autocorelations for insample forecast errors
4. Do not exceed these significance bounds for lags 1 to end
#Ljunx-Box Test to check the autocorelations of the residuals
HO: No serial correlation upto 20 lags (does not exhibit lack of fit of the model)
Ha: Serial corelation is present (the model exhibits lack of fit)
We reject the null hypothesis, if p value is less than 0.05. This test is generally done for ARIMA models
Box.test(model_Var4$residuals, lag =20, type = 'Ljung-Box')##
## Box-Ljung test
##
## data: model_Var4$residuals
## X-squared = 21.379, df = 20, p-value = 0.3751Box.test(model1_Var4$residuals, lag =20, type = 'Ljung-Box')##
## Box-Ljung test
##
## data: model1_Var4$residuals
## X-squared = 4.1403, df = 20, p-value = 0.9999Box.test(model2_Var4$residuals, lag =20, type = 'Ljung-Box')##
## Box-Ljung test
##
## data: model2_Var4$residuals
## X-squared = 22.829, df = 20, p-value = 0.2972OBSERVATIONS:
For above performed Ljunx-Box Test on all ARIMA models output, we can say that p-value is more than significance level 0.05, then there is not a statistical significance.
We conclude that there is a liitle evidence of non-zero auto-corelations in the insample forecast errors at lags 1 to 20.
So we fail to rejects the null hypothesis. Hence, we conclude that there is no serial auto corelation present between lags. Hence, the model seems to be good fit.
Test and comment on the normality of the residuals.
Here, further testing the normality by plotting Normal Q-Q plots. From below plots we observed that most of the datapoints lies on the line. Hence, we could conclude that our model produces residuals that are normal
par(mfrow = c(2,2))
qqnorm(fit_auto_train_Var4$residuals)
qqnorm(model_Var4$residuals)
qqnorm(model1_Var4$residuals)
qqnorm(model2_Var4$residuals)
Validating The Model by testing the model performance with Holdout set
Here, choosing RMSE as evaluation parameter. The lower RMSE indicates a more accurate forecast.
Below, is the comparison of model. We are fitting the model to test set which is the holdout set. And checking the accuracy using RMSE(Root mean square error) evaluation parameter.
accuracy(forecast(fit_auto_train_Var4), test3) ["Test set", "RMSE"]## [1] 4.297961#o/p - 4.297961accuracy(forecast(model1_Var4), test.sta_Var4) ["Test set", "RMSE"]## [1] 2.202662#O/P - 2.202662accuracy(forecast(model2_Var4), test.sta_Var4) ["Test set", "RMSE"]## [1] 2.203002#o/p - 2.203002accuracy(forecast(model_Var4), test.sta_Var4) ["Test set", "RMSE"]## [1] 2.202313#O/P - 2.202313NOTE:- Here, the RMSE value is less of ARIMA models compared to exponential model.
The minimum RMSE is of model_Var4.
COMMENT ON BEST MODEL AND ITS PARAMETERS
We observed the best model to be ARIMA model i.e.“model_Var4.”.
summary(model_Var4)## Series: train.sta_Var4
## ARIMA(1,0,3) with zero mean
##
## Coefficients:
## ar1 ma1 ma2 ma3
## 0.3077 -0.5011 -0.2231 -0.0916
## s.e. 0.1082 0.1092 0.0350 0.0490
##
## sigma^2 estimated as 4.805: log likelihood=-4829
## AIC=9667.99 AICc=9668.02 BIC=9696.46
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 0.001500922 2.19006 1.494088 NaN Inf 0.6431976 -0.0005031034Passing parameter order = (1,0,3) ,which means
p = 1,
d = 0
q = 3
For the best model, 1 member of lag is used as a predictor. As we transformed the series to stationary so members of differences needed for stationarity is 0. 3 are the number of lagged forecasts errors used in the prediction equation.
AIC = 9667.99, RMSE = 2.19006 which is minimum as compared to other models.
5. Forecasting on Relative Humidity at 850 hpa (RH85)
#Checking the attributes of time series
attributes(tsRH85)## $tsp
## [1] 1998.00 2004.94 365.00
##
## $class
## [1] "ts"#Plotting the series
plot(tsRH85, main = " Relative Humidity at 850 hpa (tsRH85)", col = "blue")
From the plot, we observes that there seems to have is no trend but seems to have seasonality.
Checking the statistics and visualising the missing data in the series:
#To check the missing data
plotNA.distribution(tsRH85)
#data is missing at random Here, data is missing at random.
#Impute the missing values with “na_locf” function of “imputeTS package” and visualise the imputed values in the time series
tsRH85.imp <- na_locf(tsRH85)
plotNA.imputations(tsRH85, tsRH85.imp)
#Decomposition Of Time Series
decomp4 <- decompose(tsRH85.imp)
plot(decomp4, col = "red")
OBSERVATIONS:
1)There seems to have trend. 2)We observes slighty upward trend from year 2000 onwards.
3)We observe some seasonality in the series. Seasonality describes cyclical effects due to the time of the year.
Let’s explore this seasonality pattern by plotting the decomp$seasonal components such that y-axis represents Seasonality Index and x-axis has month
#Plotting the decomposed series
par(mfrow = c(1,1))
plot(decomp4$seasonal[1:365], type ='b', xlab = 'Years', ylab = 'Seasonality Index', col = 'blue', las = 2, main = "SEASONAL DATA")
Stationarity check of time series
We could check the stationarity of time series by ADF and KPSS Tests:
- Augmented Dickey- Fuller(ADF) t-statistic test for unit root
- Kwiatkowski-Phillips-Schmidt-Shin (KPSS) for level or trend stationarity
adf.test(tsRH85.imp)## Warning in adf.test(tsRH85.imp): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: tsRH85.imp
## Dickey-Fuller = -9.223, Lag order = 13, p-value = 0.01
## alternative hypothesis: stationaryNOTE: smaller p-value, hence the series is stationary
kpss.test(tsRH85.imp, null="Trend")## Warning in kpss.test(tsRH85.imp, null = "Trend"): p-value greater than printed
## p-value##
## KPSS Test for Trend Stationarity
##
## data: tsRH85.imp
## KPSS Trend = 0.10719, Truncation lag parameter = 8, p-value = 0.1NOTE: p-value is greater, hence the series is stationary
acf(tsRH85.imp,lag.max = length(tsRH85.imp),xlab = "lag #", ylab = 'ACF',main='Statiionary Check ')
NOTE: From the both tests results, it is confirmed that the series is stationary
#CREATING MODELS AND FORECASTING: USING EXPONENTIAL SMOOTHING AND ARIMA TECHNIQUES FOR TIME SERIES FORECASTING
#TRAIN- TEST SET SPLIT
train4 <- window(tsRH85.imp, end = c(2004, 3))
test4 <- window(tsRH85.imp, start = c(2004, 4))#Model 1 : Auto Exponential Smoothening Model
set.seed(301)
fit_auto_train_Var5 <- forecast(train4)
summary(fit_auto_train_Var5)##
## Forecast method: STL + ETS(A,N,N)
##
## Model Information:
## ETS(A,N,N)
##
## Call:
## ets(y = na.interp(x), model = etsmodel, allow.multiplicative.trend = allow.multiplicative.trend)
##
## Smoothing parameters:
## alpha = 0.0811
##
## Initial states:
## l = 0.5837
##
## sigma: 0.2189
##
## AIC AICc BIC
## 10212.74 10212.75 10229.82
##
## Error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set 0.0004792866 0.2188444 0.1751376 -61.12339 84.00862 0.6284998
## ACF1
## Training set 0.3314855
##
## Forecasts:
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 2004.0082 0.6903383 0.409749880 0.9709267 0.261215353 1.1194612
## 2004.0110 0.8526915 0.571181994 1.1342011 0.422159842 1.2832232
## 2004.0137 0.7988023 0.516374644 1.0812300 0.366866457 1.2307382
## 2004.0164 0.8775044 0.594161564 1.1608473 0.444168916 1.3108399
## 2004.0192 0.5907099 0.306454776 0.8749649 0.155979229 1.0254405
## 2004.0219 0.5955454 0.310380997 0.8807098 0.159424093 1.0316667
## 2004.0247 0.7433759 0.457305153 1.0294467 0.305868423 1.1808835
## 2004.0274 0.5316621 0.244687734 0.8186364 0.092772695 0.9705515
## 2004.0301 0.7332078 0.445332788 1.0210829 0.292940940 1.1734747
## 2004.0329 0.5895441 0.300771141 0.8783171 0.147903971 1.0311842
## 2004.0356 0.4586290 0.168960889 0.7482970 0.015619871 0.9016381
## 2004.0384 0.6023033 0.311742885 0.8928638 0.157929478 1.0466772
## 2004.0411 0.8161813 0.524731179 1.1076313 0.370446830 1.2619157
## 2004.0438 0.7291790 0.436842035 1.0215160 0.282088177 1.1762699
## 2004.0466 0.4441800 0.150958805 0.7374013 -0.004263142 0.8926232
## 2004.0493 0.6915449 0.397442088 0.9856477 0.241753460 1.1413364
## 2004.0521 0.5298240 0.234842183 0.8248057 0.078688268 0.9809596
## 2004.0548 0.3555576 0.059699523 0.6514157 -0.096918297 0.8080335
## 2004.0575 0.4860708 0.189338911 0.7828026 0.032258557 0.9398830
## 2004.0603 0.6965724 0.398969318 0.9941754 0.241427788 1.1517169
## 2004.0630 0.5864193 0.287947636 0.8848910 0.129946275 1.0428923
## 2004.0658 0.7472774 0.447939608 1.0466152 0.289479751 1.2050751
## 2004.0685 0.5206612 0.220459812 0.8208626 0.061542782 0.9797797
## 2004.0712 0.6014621 0.300399587 0.9025247 0.141026695 1.0618976
## 2004.0740 0.4397424 0.137821111 0.7416636 -0.022006343 0.9014911
## 2004.0767 0.5056265 0.202849017 0.8084040 0.042568291 0.9686847
## 2004.0795 0.7315324 0.427901046 1.0351637 0.267168326 1.1958964
## 2004.0822 0.8532957 0.548812953 1.1577785 0.387629506 1.3189620
## 2004.0849 0.7203875 0.415055656 1.0257194 0.253422740 1.1873523
## 2004.0877 0.6182861 0.312107588 0.9244647 0.150026448 1.0865459
## 2004.0904 0.6510228 0.343999838 0.9580457 0.181471711 1.1205738
## 2004.0932 0.7848989 0.477033929 1.0927639 0.314060041 1.2557378
## 2004.0959 0.5916016 0.282896815 0.9003064 0.119478381 1.0637248
## 2004.0986 0.5299656 0.220423318 0.8395078 0.056561544 1.0033696
## 2004.1014 0.4878031 0.177425579 0.7981806 0.013121663 0.9624845
## 2004.1041 0.5809627 0.269752263 0.8921732 0.105007390 1.0569181
## 2004.1068 0.6216550 0.309613797 0.9336963 0.144429145 1.0988809
## 2004.1096 0.7530308 0.440160968 1.0659006 0.274537704 1.2315238
## 2004.1123 0.7644668 0.450770642 1.0781630 0.284709925 1.2442237
## 2004.1151 0.6701589 0.355638575 0.9846793 0.189141553 1.1511763
## 2004.1178 0.7938439 0.478501494 1.1091863 0.311569309 1.2761185
## 2004.1205 0.6830619 0.366899560 0.9992242 0.199533343 1.1665904
## 2004.1233 0.4194583 0.102478209 0.7364384 -0.065320917 0.9042375
## 2004.1260 0.5918362 0.274040447 0.9096320 0.105809525 1.0778629
## 2004.1288 0.7957964 0.477186984 1.1144057 0.308525373 1.2830673
## 2004.1315 0.7070350 0.387614120 1.0264559 0.218522915 1.1955471
## 2004.1342 0.5851654 0.264935034 0.9053957 0.095415325 1.0749154
## 2004.1370 0.4927723 0.171734488 0.8138100 0.001787355 0.9837572
## 2004.1397 0.5161260 0.194282863 0.8379692 0.023909379 1.0083427
## 2004.1425 0.6292570 0.306610447 0.9519036 0.135811675 1.1227023
## 2004.1452 0.7529398 0.429491829 1.0763877 0.258268826 1.2476107
## 2004.1479 0.7023877 0.378140371 1.0266351 0.206494186 1.1982813
## 2004.1507 0.8628819 0.537837124 1.1879267 0.365768797 1.3599951
## 2004.1534 0.6068324 0.280992059 0.9326727 0.108502624 1.1051621
## 2004.1562 0.5219131 0.195279282 0.8485470 0.022369764 1.0214565
## 2004.1589 0.7264967 0.399071259 1.0539222 0.225742677 1.2272508
## 2004.1616 0.4924090 0.164193834 0.8206243 -0.009552803 0.9943709
## 2004.1644 0.4743785 0.145375452 0.8033815 -0.028788236 0.9775452
## 2004.1671 0.8039815 0.474192506 1.1337705 0.299612764 1.3083502
## 2004.1699 0.6172734 0.286700292 0.9478464 0.111705484 1.1228412
## 2004.1726 0.6384796 0.307124356 0.9698349 0.131715466 1.1452438
## 2004.1753 0.7241334 0.391997720 1.0562690 0.216175722 1.2320910
## 2004.1781 0.6788397 0.345925449 1.0117539 0.169691312 1.1879880
## 2004.1808 0.8006346 0.466943634 1.1343255 0.290298318 1.3109708
## 2004.1836 0.6075687 0.273102838 0.9420346 0.096047300 1.1190901
## 2004.1863 0.4655810 0.130341949 0.8008200 -0.047122864 0.9782848
## 2004.1890 0.3681486 0.032138198 0.7041589 -0.145734948 0.8820321
## 2004.1918 0.3647278 0.027947795 0.7015077 -0.150332749 0.8797883
## 2004.1945 0.6882615 0.350713663 1.0258093 0.172026651 1.2044963
## 2004.1973 0.7578975 0.419583639 1.0962114 0.240491080 1.2753040
## 2004.2000 0.6855802 0.346501916 1.0246584 0.167004727 1.2041556
## 2004.2027 0.7235325 0.383691545 1.0633734 0.203790636 1.2432743
## 2004.2055 0.6914548 0.350852987 1.0320567 0.170549262 1.2123604
## 2004.2082 0.6563413 0.314980170 0.9977023 0.134274527 1.1784080
## 2004.2110 0.5914371 0.249318417 0.9335557 0.068211747 1.1146624
## 2004.2137 0.6393040 0.296429444 0.9821785 0.114922635 1.1636853
## 2004.2164 0.4569210 0.113292303 0.8005498 -0.068613766 0.9824559
## 2004.2192 0.5409456 0.196564244 0.8853269 0.014259789 1.0676313
## 2004.2219 0.6058790 0.260746769 0.9510113 0.078044797 1.1337132
## 2004.2247 0.6733852 0.327503665 1.0192667 0.144405039 1.2023654
## 2004.2274 0.5141911 0.167561911 0.8608203 -0.015932512 1.0443148
## 2004.2301 0.4402605 0.092885217 0.7876358 -0.091004150 0.9715252
## 2004.2329 0.6333339 0.285214163 0.9814537 0.100930698 1.1657371
## 2004.2356 0.6125622 0.263699533 0.9614248 0.079022810 1.1461015
## 2004.2384 0.5123836 0.162779630 0.8619875 -0.022289514 1.0470566
## 2004.2411 0.7413918 0.391048083 1.0917354 0.205587348 1.2771962
## 2004.2438 0.7967543 0.445672503 1.1478362 0.259821003 1.3336877
## 2004.2466 0.9064421 0.554623635 1.2582606 0.368382187 1.4445020
## 2004.2493 0.8315019 0.478948390 1.1840555 0.292317811 1.3706861
## 2004.2521 0.5809850 0.227697936 0.9342722 0.040679035 1.1212911
## 2004.2548 0.6727809 0.318761766 1.0268001 0.131355349 1.2142065
## 2004.2575 0.6503021 0.295552432 1.0050518 0.107759297 1.1928449
## 2004.2603 0.4831357 0.127657012 0.8386144 -0.060522045 1.0267935
## 2004.2630 0.5194179 0.163211705 0.8756242 -0.025352485 1.0641884
## 2004.2658 0.5233246 0.166392287 0.8802569 -0.022556252 1.0692054
## 2004.2685 0.6681129 0.310456011 1.0257697 0.121123905 1.2151018
## 2004.2712 0.5843268 0.225946832 0.9427068 0.036231934 1.1324217
## 2004.2740 0.4994809 0.140379244 0.8585825 -0.049717675 1.0486794
## 2004.2767 0.5626058 0.202783920 0.9224276 0.012305746 1.1129058
## 2004.2795 0.5115828 0.151042197 0.8721234 -0.039816471 1.0629821
## 2004.2822 0.6927907 0.331532791 1.0540487 0.140294386 1.2452871
## 2004.2849 0.7145352 0.352561294 1.0765090 0.160943905 1.2681264
## 2004.2877 0.6984662 0.335777853 1.0611546 0.143782228 1.2531502
## 2004.2904 0.4925580 0.129156482 0.8559594 -0.063216635 1.0483325
## 2004.2932 0.5414262 0.177313033 0.9055394 -0.015436837 1.0982892
## 2004.2959 0.5121307 0.147307241 0.8769542 -0.045818647 1.0700801
## 2004.2986 0.6199850 0.254452552 0.9855174 0.060951377 1.1790186
## 2004.3014 0.7866214 0.420381434 1.1528614 0.226505698 1.3467371
## 2004.3041 0.7681789 0.401232672 1.1351250 0.206983097 1.3293746
## 2004.3068 0.6904692 0.322818131 1.0581202 0.128195436 1.2527429
## 2004.3096 0.5434475 0.175092985 0.9118020 -0.019902116 1.1067971
## 2004.3123 0.7219339 0.352877230 1.0909906 0.157510432 1.2863574
## 2004.3151 0.6435051 0.273747606 1.0132626 0.078009817 1.2090004
## 2004.3178 0.7618530 0.391395991 1.1323099 0.195287913 1.3284180
## 2004.3205 0.7427656 0.371610425 1.1139207 0.175132756 1.3103984
## 2004.3233 0.7982716 0.426419628 1.1701237 0.229573062 1.3669702
## 2004.3260 0.7701508 0.397603209 1.1426984 0.200388436 1.3399131
## 2004.3288 0.8141442 0.440902400 1.1873861 0.243320105 1.3849684
## 2004.3315 0.5940443 0.220109452 0.9679791 0.022160319 1.1659282
## 2004.3342 0.4057537 0.031127164 0.7803802 -0.167188129 0.9786955
## 2004.3370 0.6349567 0.259639780 1.0102736 0.060959002 1.2089544
## 2004.3397 0.6912215 0.315215466 1.0672276 0.116169874 1.2662732
## 2004.3425 0.7004929 0.323798939 1.0771869 0.124389200 1.2765966
## 2004.3452 0.5643836 0.187003011 0.9417642 -0.012770211 1.1415374
## 2004.3479 0.5971756 0.219109606 0.9752416 0.018973560 1.1753776
## 2004.3507 0.6025342 0.223784026 0.9812843 0.023285814 1.1817825
## 2004.3534 0.6614977 0.282064672 1.0409308 0.081204947 1.2417905
## 2004.3562 0.5065863 0.126471529 0.8867010 -0.074749059 1.0879216
## 2004.3589 0.4612126 0.080417412 0.8420078 -0.121163394 1.0435886
## 2004.3616 0.7513036 0.369829129 1.1327781 0.167888748 1.3347184
## 2004.3644 0.6670635 0.284910993 1.0492160 0.082611675 1.2515153
## 2004.3671 0.6735360 0.290706688 1.0563654 0.088049070 1.2590230
## 2004.3699 0.7291713 0.345666321 1.1126763 0.142651035 1.3156916
## 2004.3726 0.6910850 0.306905576 1.0752645 0.103533251 1.2786368
## 2004.3753 0.7352996 0.350446900 1.1201524 0.146718162 1.3238811
## 2004.3781 0.8032623 0.417737397 1.1887871 0.213652868 1.3928716
## 2004.3808 0.7303742 0.344178386 1.1165700 0.139738685 1.3210097
## 2004.3836 0.6088465 0.221980968 0.9957121 0.017186711 1.2005063
## 2004.3863 0.7944344 0.406900268 1.1819686 0.201752069 1.3871168
## 2004.3890 0.7295727 0.341371102 1.1177744 0.135869570 1.3232759
## 2004.3918 0.7368402 0.347972257 1.1257082 0.142117998 1.3315624
## 2004.3945 0.8427149 0.453181781 1.2322480 0.246975398 1.4384544
## 2004.3973 0.8203734 0.430176247 1.2105706 0.223618341 1.4171285
## 2004.4000 0.8536087 0.462748591 1.2444688 0.255839758 1.4513776
## 2004.4027 0.8503690 0.458847115 1.2418909 0.251587951 1.4491500
## 2004.4055 0.8417291 0.449546521 1.2339116 0.241937617 1.4415205
## 2004.4082 0.8615636 0.468721437 1.2544057 0.260763380 1.4623637
## 2004.4110 0.8056894 0.412188821 1.1991900 0.203882197 1.4074966
## 2004.4137 0.6987824 0.304624493 1.0929404 0.095969884 1.3015950
## 2004.4164 0.7335847 0.338770457 1.1283989 0.129768442 1.3374009
## 2004.4192 0.8435064 0.448037003 1.2389758 0.238688160 1.4483246
## 2004.4219 0.7866572 0.390533696 1.1827806 0.180838597 1.3924757
## 2004.4247 0.9348751 0.538098595 1.3316516 0.328057811 1.5416923
## 2004.4274 0.8856140 0.488185546 1.2830424 0.277799645 1.4934283
## 2004.4301 0.8839949 0.485915648 1.2820742 0.275185196 1.4928047
## 2004.4329 0.8187265 0.419997415 1.2174556 0.208922975 1.4285301
## 2004.4356 0.8088582 0.409480350 1.2082361 0.198062481 1.4196539
## 2004.4384 0.7660536 0.366028038 1.1660792 0.154267296 1.3778399
## 2004.4411 0.8003651 0.399692894 1.2010373 0.187589834 1.4131404
## 2004.4438 0.7534894 0.352171595 1.1548073 0.139726768 1.3672521
## 2004.4466 0.8263503 0.424387868 1.2283127 0.211601824 1.4410987
## 2004.4493 0.8239641 0.421358152 1.2265700 0.208231437 1.4396968
## 2004.4521 0.7992179 0.395969457 1.2024664 0.182502615 1.4159332
## 2004.4548 0.7931283 0.389238372 1.1970183 0.175431943 1.4108247
## 2004.4575 0.7532842 0.348753763 1.1578146 0.134608286 1.3719601
## 2004.4603 0.7992506 0.394080742 1.2044205 0.179596752 1.4189045
## 2004.4630 0.7382550 0.332446609 1.1440633 0.117624641 1.3588853
## 2004.4658 0.6878402 0.281394347 1.0942860 0.066234932 1.3094454
## 2004.4685 0.8700466 0.462964290 1.2771288 0.247467955 1.4926252
## 2004.4712 0.8488557 0.441137922 1.2565734 0.225305194 1.4724061
## 2004.4740 0.7790035 0.370651294 1.1873557 0.154482697 1.4035243
## 2004.4767 0.8413452 0.432359472 1.2503309 0.215855526 1.4668348
## 2004.4795 0.7740973 0.364479076 1.1837155 0.147640300 1.4005543
## 2004.4822 0.7427011 0.332451397 1.1529509 0.115278306 1.3701240
## 2004.4849 0.8324691 0.421588768 1.2433494 0.204081877 1.4608563
## 2004.4877 0.8642048 0.452694915 1.2757147 0.234854735 1.4935549
## 2004.4904 0.7045009 0.292362398 1.1166395 0.074189439 1.3348124
## 2004.4932 0.6450355 0.232269257 1.0578017 0.013764025 1.2763069
## 2004.4959 0.7268628 0.313469896 1.1402558 0.094632896 1.3590928
## 2004.4986 0.7159586 0.301939898 1.1299773 0.082771632 1.3491456
## 2004.5014 0.7945505 0.379906935 1.2091940 0.160407904 1.4286930
## 2004.5041 0.7477166 0.332449154 1.1629840 0.112619854 1.3828133
## 2004.5068 0.7089673 0.293076889 1.1248577 0.072917816 1.3450167
## 2004.5096 0.7641209 0.347608498 1.1806333 0.127120145 1.4011217
## 2004.5123 0.7028242 0.285690737 1.1199578 0.064873596 1.3407749
## 2004.5151 0.7457759 0.328022199 1.1635296 0.106876758 1.3846750
## 2004.5178 0.7400395 0.321666580 1.1584125 0.100193326 1.3798857
## 2004.5205 0.7821120 0.363120763 1.2011033 0.141320180 1.4229039
## 2004.5233 0.8162387 0.396629961 1.2358474 0.174502533 1.4579748
## 2004.5260 0.8415881 0.421362877 1.2618133 0.198909082 1.4842671
## 2004.5288 0.8292412 0.408400397 1.2500821 0.185620714 1.4728618
## 2004.5315 0.8331482 0.411692631 1.2546037 0.188587536 1.4777088
## 2004.5342 0.7926687 0.370599304 1.2147381 0.147169271 1.4381681
## 2004.5370 0.7920329 0.369350550 1.2147152 0.145596051 1.4384697
## 2004.5397 0.7814203 0.358125980 1.2047147 0.134047485 1.4287932
## 2004.5425 0.7803950 0.356489484 1.2043005 0.132087460 1.4287025
## 2004.5452 0.7513843 0.326868536 1.1759001 0.102143450 1.4006252
## 2004.5479 0.8256343 0.400509116 1.2507595 0.175461431 1.4758072
## 2004.5507 0.8094534 0.383719631 1.2351871 0.158349808 1.4605569
## 2004.5534 0.7731100 0.346768624 1.1994514 0.121077124 1.4251429
## 2004.5562 0.7743631 0.347414952 1.2013113 0.121402233 1.4273241
## 2004.5589 0.8138349 0.386280798 1.2413891 0.159947315 1.4677225
## 2004.5616 0.8141966 0.386037437 1.2423558 0.159383644 1.4690096
## 2004.5644 0.7456027 0.316839240 1.1743661 0.089865590 1.4013398
## 2004.5671 0.8361732 0.406806403 1.2655400 0.179513345 1.4928331
## 2004.5699 0.8072868 0.377317441 1.2372561 0.149705424 1.4648681
## 2004.5726 0.7594244 0.328853399 1.1899954 0.100922869 1.4179260
## 2004.5753 0.7964734 0.365301555 1.2276453 0.137052957 1.4558939
## 2004.5781 0.8088478 0.377075930 1.2406197 0.148509705 1.4691859
## 2004.5808 0.7317502 0.299379164 1.1641213 0.070495754 1.3930047
## 2004.5836 0.8617991 0.428829652 1.2947685 0.199629496 1.5239686
## 2004.5863 0.8489999 0.415432942 1.2825668 0.185916477 1.5120833
## 2004.5890 0.7503520 0.316188342 1.1845156 0.086356004 1.4143479
## 2004.5918 0.7935974 0.358837859 1.2283569 0.128690081 1.4585046
## 2004.5945 0.6962466 0.260892000 1.1316011 0.030429213 1.3620639
## 2004.5973 0.7197816 0.283832779 1.1557304 0.053055413 1.3865078
## 2004.6000 0.7477828 0.311240574 1.1843251 0.080149058 1.4154166
## 2004.6027 0.7706745 0.333539610 1.2078094 0.102134370 1.4392147
## 2004.6055 0.7626004 0.324873614 1.2003271 0.093155075 1.4320456
## 2004.6082 0.8835149 0.445197108 1.3218327 0.213165693 1.5538641
## 2004.6110 0.8246786 0.385770591 1.2635866 0.153426722 1.4959305
## 2004.6137 0.8283721 0.388874673 1.2678696 0.156218768 1.5005255
## 2004.6164 0.7917123 0.351626135 1.2317984 0.118658613 1.4647659
## 2004.6192 0.7649834 0.324309378 1.2056574 0.091030655 1.4389361
## 2004.6219 0.6603092 0.219048151 1.1015703 -0.014541357 1.3351598
## 2004.6247 0.7787516 0.336904179 1.2205990 0.103004297 1.4544988
## 2004.6274 0.8079520 0.365519094 1.2503849 0.131309251 1.4845948
## 2004.6301 0.7304504 0.287432707 1.1734681 0.052913311 1.4079875
## 2004.6329 0.8681154 0.424513729 1.3117171 0.189685188 1.5465456
## 2004.6356 0.9154196 0.471234692 1.3596045 0.236097413 1.5947418
## 2004.6384 0.8228060 0.378038698 1.2675734 0.142593087 1.5030190
## 2004.6411 0.8252123 0.379863265 1.2705613 0.144109724 1.5063149
## 2004.6438 0.7093002 0.263370269 1.1552302 0.027309200 1.3912913
## 2004.6466 0.7411020 0.294591859 1.1876122 0.058223662 1.4239804
## 2004.6493 0.8037303 0.356640699 1.2508199 0.119965773 1.4874948
## 2004.6521 0.7398815 0.292213287 1.1875498 0.055232028 1.4245311
## 2004.6548 0.8760843 0.427838128 1.3243305 0.190550932 1.5616177
## 2004.6575 0.7259528 0.277129388 1.1747761 0.039536650 1.4123689
## 2004.6603 0.7167740 0.267374236 1.1661739 0.029476347 1.4040717
## 2004.6630 0.8248458 0.374870270 1.2748213 0.136667622 1.5130239
## 2004.6658 0.9069702 0.456419740 1.3575207 0.217912722 1.5960277
## 2004.6685 0.7036291 0.252504333 1.1547538 0.013693332 1.3935648
## 2004.6712 0.7102652 0.258566999 1.1619635 0.019452402 1.4010780
## 2004.6740 0.7709246 0.318653578 1.2231956 0.079235770 1.4626134
## 2004.6767 0.7111675 0.258324462 1.1640106 0.018603827 1.4037312
## 2004.6795 0.7054254 0.252010973 1.1588398 0.011987892 1.3988628
## 2004.6822 0.8331998 0.379214789 1.2871848 0.138889645 1.5275099
## 2004.6849 0.7490313 0.294476421 1.2035862 0.053849590 1.4442131
## 2004.6877 0.6214483 0.166324166 1.0765723 -0.074603972 1.3175005
## 2004.6904 0.7269742 0.271281633 1.1826668 0.030052563 1.4238958
## 2004.6932 0.6699687 0.213708394 1.1262290 -0.027821232 1.3677587
## 2004.6959 0.5388099 0.081982562 0.9956373 -0.159847247 1.2374671
## 2004.6986 0.7514977 0.294103942 1.2088914 0.051974322 1.4510210
## 2004.7014 0.5616630 0.103703596 1.0196224 -0.138725463 1.2620514
## 2004.7041 0.6117862 0.153261837 1.0703105 -0.089466293 1.3130387
## 2004.7068 0.6306124 0.171523826 1.0897011 -0.071503006 1.3327279
## 2004.7096 0.6892057 0.229553475 1.1488578 -0.013771693 1.3921830
## 2004.7123 0.6998181 0.239603040 1.1600332 -0.004020099 1.4036563
## 2004.7151 0.6083076 0.147530358 1.0690849 -0.096390387 1.3130056
## 2004.7178 0.6170926 0.155753813 1.0784313 -0.088464176 1.3226493
## 2004.7205 0.5743151 0.112415524 1.0362147 -0.132099348 1.2807296
## 2004.7233 0.7745075 0.312047734 1.2369672 0.067236341 1.4817786
## 2004.7260 0.7957426 0.332723401 1.2587618 0.087615843 1.5038694
## 2004.7288 0.7035257 0.239947752 1.1671037 -0.005455612 1.4125071
## 2004.7315 0.5865873 0.122451165 1.0507234 -0.123247649 1.2964222
## 2004.7342 0.6275986 0.162905075 1.0922922 -0.083088835 1.3382861
## 2004.7370 0.5183230 0.053072647 0.9835733 -0.193216004 1.2298620
## 2004.7397 0.5650978 0.099291327 1.0309042 -0.147291713 1.2774873
## 2004.7425 0.7053450 0.238983098 1.1717069 -0.007893981 1.4185840
## 2004.7452 0.6431620 0.176245344 1.1100787 -0.070925424 1.3572495
## 2004.7479 0.6536181 0.186147299 1.1210890 -0.061316809 1.3685531
## 2004.7507 0.6844069 0.216382609 1.1524312 -0.031374491 1.4001883
## 2004.7534 0.5749306 0.106353492 1.0435077 -0.141696255 1.2915575
## 2004.7562 0.8002850 0.331155678 1.2694143 0.082813629 1.5177563
## 2004.7589 0.6988698 0.229188968 1.1685506 -0.019445039 1.4171846
## 2004.7616 0.7148912 0.244659479 1.1851229 -0.004266143 1.4340485
## 2004.7644 0.6205327 0.149750738 1.0913146 -0.099466159 1.3405315
## 2004.7671 0.5049602 0.033628717 0.9762917 -0.215879114 1.2257996
## 2004.7699 0.3970287 -0.074851754 0.8689092 -0.324650182 1.1187076
## 2004.7726 0.7000421 0.227613376 1.1724709 -0.022475310 1.4225596
## 2004.7753 0.7136026 0.240626188 1.1865791 -0.009752419 1.4369577
## 2004.7781 0.5398700 0.066346471 1.0133934 -0.184321722 1.2640616
## 2004.7808 0.7454226 0.271352677 1.2194925 0.020395232 1.4704499
## 2004.7836 0.5409381 0.066322411 1.0155538 -0.184923953 1.2668001
## 2004.7863 0.5875822 0.112421375 1.0627430 -0.139113576 1.3142780
## 2004.7890 0.3789150 -0.096790389 0.8546203 -0.348613597 1.1064435
## 2004.7918 0.3720228 -0.104226427 0.8482721 -0.356337561 1.1003832
## 2004.7945 0.3954460 -0.081346566 0.8722385 -0.333745299 1.1246373
## 2004.7973 0.5451753 0.067840069 1.0225105 -0.184845935 1.2751965
## 2004.8000 0.6780347 0.200157380 1.1559119 -0.052815568 1.4088849
## 2004.8027 0.6980870 0.219668331 1.1765058 -0.033591237 1.4297653
## 2004.8055 0.5978873 0.118927737 1.0768468 -0.134618127 1.3303927
## 2004.8082 0.5589633 0.079463518 1.0384630 -0.174368318 1.2922949
## 2004.8110 0.4477275 -0.032311881 0.9277668 -0.286429369 1.1818843
## 2004.8137 0.7220120 0.241433597 1.2025903 -0.012969221 1.4569931
## 2004.8164 0.5066179 0.025501091 0.9877346 -0.229186738 1.2424224
## 2004.8192 0.6161771 0.134522567 1.0978317 -0.120449953 1.3528042
## 2004.8219 0.4966312 0.014439423 0.9788229 -0.240817472 1.2340798
## 2004.8247 0.6021744 0.119446085 1.0849028 -0.136094867 1.3404437
## 2004.8274 0.5427273 0.059462945 1.0259917 -0.196361751 1.2818163
## 2004.8301 0.7179324 0.234132611 1.2017321 -0.021975513 1.4578403
## 2004.8329 0.6736324 0.189297819 1.1579670 -0.067093420 1.4143582
## 2004.8356 0.4342586 -0.050610198 0.9191274 -0.307284240 1.1758015
## 2004.8384 0.3760001 -0.109402372 0.8614025 -0.366358905 1.1183591
## 2004.8411 0.6053154 0.119379931 1.0912509 -0.137858783 1.3484896
## 2004.8438 0.6804294 0.193961468 1.1668974 -0.063559118 1.4244180
## 2004.8466 0.5143903 0.027390482 1.0013902 -0.230411668 1.2591923
## 2004.8493 0.5897788 0.102247645 1.0773100 -0.155835762 1.3353934
## 2004.8521 0.3820814 -0.105980444 0.8701433 -0.364344801 1.1285077
## 2004.8548 0.5320945 0.043502490 1.0206866 -0.215142512 1.2793316
## 2004.8575 0.5222711 0.033149498 1.0113927 -0.225775845 1.2703181
## 2004.8603 0.7177437 0.228093060 1.2073943 -0.031112321 1.4665997
## 2004.8630 0.8597176 0.369538584 1.3498967 0.110053468 1.6093818
## 2004.8658 0.6072848 0.116577917 1.0979918 -0.143186634 1.3577563
## 2004.8685 0.5255507 0.034316470 1.0167849 -0.225727215 1.2768286
## 2004.8712 0.5310275 0.039266522 1.0227884 -0.221055998 1.2831109
## 2004.8740 0.5683224 0.076035284 1.0606095 -0.184565773 1.3212106
## 2004.8767 0.8134740 0.320661296 1.3062867 0.059782001 1.5671660
## 2004.8795 0.6767441 0.183406351 1.1700819 -0.077750887 1.4312391
## 2004.8822 0.5357548 0.041892537 1.0296170 -0.219542348 1.2910519
## 2004.8849 0.6448286 0.150442393 1.1392148 -0.111269845 1.4009270
## 2004.8877 0.6667075 0.171797943 1.1616171 -0.090191354 1.4236064
## 2004.8904 0.5887509 0.093318499 1.0841833 -0.168947564 1.3464493
## 2004.8932 0.5930738 0.097119097 1.0890284 -0.165423440 1.3515710
## 2004.8959 0.6372996 0.140823221 1.1337760 -0.121995500 1.3965947
## 2004.8986 0.6209683 0.123970789 1.1179659 -0.139123827 1.3810605
## 2004.9014 0.5032821 0.005763911 1.0008003 -0.257606308 1.2641705
## 2004.9041 0.5941201 0.096081838 1.0921584 -0.167563698 1.3558039
## 2004.9068 0.5290517 0.030493873 1.0276095 -0.233426693 1.2915301
## 2004.9096 0.5314034 0.032326628 1.0304803 -0.231868681 1.2946756
## 2004.9123 0.7038493 0.204254021 1.2034446 -0.060215746 1.4679144
## 2004.9151 0.9054951 0.405381877 1.4056083 0.140637937 1.6703522
## 2004.9178 0.7163707 0.215740139 1.2170013 -0.049277691 1.4820192
## 2004.9205 0.5719845 0.070837060 1.0731320 -0.194454376 1.3384234
## 2004.9233 0.6209071 0.119243292 1.1225708 -0.146321469 1.3881356
## 2004.9260 0.5314784 0.029298857 1.0336580 -0.236538948 1.2994958
## 2004.9288 0.4856011 -0.017093722 0.9882959 -0.283204291 1.2544065
## 2004.9315 0.5517062 0.048496624 1.0549158 -0.217886429 1.3212988
## 2004.9342 0.2449924 -0.258731417 0.7487161 -0.525386677 1.0153714
## 2004.9370 0.5088668 0.004629349 1.0131043 -0.262297839 1.2800315
## 2004.9397 0.6630588 0.158308196 1.1678094 -0.108890643 1.4350083
## 2004.9425 0.6137802 0.108516887 1.1190434 -0.158953328 1.3865136
## 2004.9452 0.5375032 0.031727861 1.0432786 -0.236013455 1.3110199
## 2004.9479 0.5150377 0.008750674 1.0213247 -0.259261469 1.2893368
## 2004.9507 0.6270537 0.120255657 1.1338518 -0.148027038 1.4021345
## 2004.9534 0.5061101 -0.001198576 1.0134187 -0.269751552 1.2819717
## 2004.9562 0.5704559 0.062637210 1.0782746 -0.206185774 1.3470976
## 2004.9589 0.4453888 -0.062939450 0.9537171 -0.332032173 1.2228098
## 2004.9616 0.4662459 -0.042591379 0.9750832 -0.311953569 1.2444454
## 2004.9644 0.6087059 0.099360062 1.1180517 -0.170271326 1.3876831
## 2004.9671 0.6229421 0.113088215 1.1327959 -0.156812104 1.4026962
## 2004.9699 0.4400719 -0.070289419 0.9504333 -0.340458400 1.2206023
## 2004.9726 0.6059110 0.095042625 1.1167794 -0.175394751 1.3872167
## 2004.9753 0.6360319 0.124657059 1.1474068 -0.146048446 1.4181123
## 2004.9781 0.5470015 0.035120619 1.0588824 -0.235852750 1.3298557
## 2004.9808 0.5174789 0.005092478 1.0298653 -0.266148491 1.3011062
## 2004.9836 0.6443095 0.131418139 1.1572009 -0.140090165 1.4287092
## 2004.9863 0.5288986 0.015502732 1.0422945 -0.256272645 1.3140699
## 2004.9890 0.5947417 0.080841810 1.1086417 -0.191200377 1.3806838
## 2004.9918 0.3032528 -0.211150637 0.8176563 -0.483459373 1.0899650
## 2004.9945 0.5454123 0.030505870 1.0603188 -0.242069155 1.3328939
## 2004.9973 0.5047455 -0.010663501 1.0201545 -0.283504554 1.2929956
## 2005.0000 0.5453453 0.029434249 1.0612564 -0.243672573 1.3343632
## 2005.0027 0.7679888 0.251576168 1.2844014 -0.021796166 1.5577738
## 2005.0055 0.5411754 0.024261720 1.0580891 -0.249375867 1.3317267
## 2005.0082 0.6903383 0.172923983 1.2077526 -0.100978600 1.4816552
## 2005.0110 0.8526915 0.334777137 1.3706059 0.060609813 1.6447733
## 2005.0137 0.7988023 0.280388305 1.3172164 0.005956497 1.5916482
## 2005.0164 0.8775044 0.358591249 1.3964176 0.083895210 1.6711136
## 2005.0192 0.5907099 0.071298019 1.1101217 -0.203661996 1.3850817
## 2005.0219 0.5955454 0.075635357 1.1154554 -0.199588381 1.3906791
## 2005.0247 0.7433759 0.222968217 1.2637837 -0.052518992 1.5392709
## 2005.0274 0.5316621 0.010757116 1.0525670 -0.264993313 1.3283175
## 2005.0301 0.7332078 0.211806125 1.2546096 -0.064207272 1.5306230
## 2005.0329 0.5895441 0.067646096 1.1114421 -0.208630018 1.3877182
## 2005.0356 0.4586290 -0.063764850 0.9810228 -0.340303432 1.2575614
## 2005.0384 0.6023033 0.079414166 1.1251925 -0.197386636 1.4019933
## 2005.0411 0.8161813 0.292797215 1.3395653 0.015734443 1.6166281
## 2005.0438 0.7291790 0.205300588 1.2530575 -0.072023908 1.5303820
## 2005.0466 0.4441800 -0.080192343 0.9685524 -0.357778316 1.2461384
## 2005.0493 0.6915449 0.166679046 1.2164108 -0.111168157 1.4942580
## 2005.0521 0.5298240 0.004465076 1.0551828 -0.273643113 1.3332910
## 2005.0548 0.3555576 -0.170293799 0.8814091 -0.448662729 1.1597780
## 2005.0575 0.4860708 -0.040272753 1.0124143 -0.318902179 1.2910437
## 2005.0603 0.6965724 0.169737208 1.2234075 -0.109152472 1.5022972
## 2005.0630 0.5864193 0.059092994 1.1137456 -0.220056697 1.3928953
## 2005.0658 0.7472774 0.219460370 1.2750944 -0.059949089 1.5545039
## 2005.0685 0.5206612 -0.007646063 1.0489685 -0.287315050 1.3286375
## 2005.0712 0.6014621 0.072665050 1.1302592 -0.207263224 1.4101875
## 2005.0740 0.4397424 -0.089544090 0.9690288 -0.369731410 1.2492161
## 2005.0767 0.5056265 -0.024148831 1.0354019 -0.304594959 1.3158480
## 2005.0795 0.7315324 0.201268587 1.2617962 -0.079436110 1.5425009
## 2005.0822 0.8532957 0.322543938 1.3840475 0.041580910 1.6650106
## 2005.0849 0.7203875 0.189148159 1.2516268 -0.092072963 1.5328480
## 2005.0877 0.6182861 0.086559701 1.1500126 -0.194919278 1.4314916
## 2005.0904 0.6510228 0.118809673 1.1832359 -0.162926927 1.4649725
## 2005.0932 0.7848989 0.252199614 1.3175983 -0.029794372 1.5995922
## 2005.0959 0.5916016 0.058416496 1.1247867 -0.223834641 1.4070378
## 2005.0986 0.5299656 -0.003704841 1.0636360 -0.286212895 1.3461440
## 2005.1014 0.4878031 -0.046352238 1.0219584 -0.329116975 1.3047231
## 2005.1041 0.5809627 0.046322986 1.1156025 -0.236698202 1.3986237
## 2005.1068 0.6216550 0.086531275 1.1567788 -0.196746132 1.4400562
## 2005.1096 0.7530308 0.217423432 1.2886381 -0.066109962 1.5721715
## 2005.1123 0.7644668 0.228376340 1.3005573 -0.055412810 1.5843464
## 2005.1151 0.6701589 0.133585770 1.2067321 -0.150458906 1.4907768
## 2005.1178 0.7938439 0.256788467 1.3308993 -0.027511505 1.6151993
## 2005.1205 0.6830619 0.145524606 1.2205991 -0.139030433 1.5051542
## 2005.1233 0.4194583 -0.118560362 0.9574770 -0.403370239 1.2422868
## 2005.1260 0.5918362 0.053336585 1.1303359 -0.231727903 1.4154003
## 2005.1288 0.7957964 0.256816173 1.3347765 -0.028502699 1.6200954
## 2005.1315 0.7070350 0.167574715 1.2464953 -0.117998314 1.5320683
## 2005.1342 0.5851654 0.045225406 1.1251054 -0.240601555 1.4109323
## 2005.1370 0.4927723 -0.047646979 1.0331915 -0.333727645 1.3192722
## 2005.1397 0.5161260 -0.024772044 1.0570241 -0.311106191 1.3433583
## 2005.1425 0.6292570 0.087880514 1.1706335 -0.198706890 1.4572209
## 2005.1452 0.7529398 0.211085296 1.2947943 -0.075755141 1.5816347
## 2005.1479 0.7023877 0.160055679 1.2447198 -0.127037567 1.5318130
## 2005.1507 0.8628819 0.320072727 1.4056911 0.032726893 1.6930370
## 2005.1534 0.6068324 0.063546425 1.1501183 -0.224051775 1.4377165
## 2005.1562 0.5219131 -0.021849108 1.0656754 -0.309699453 1.3535257
## 2005.1589 0.7264967 0.182258606 1.2707349 -0.105843663 1.5588372
## 2005.1616 0.4924090 -0.052304576 1.0371227 -0.340658549 1.3254766
## 2005.1644 0.4743785 -0.070810196 1.0195672 -0.359415653 1.3081726
## 2005.1671 0.8039815 0.258318151 1.3496448 -0.030538571 1.6385015
## 2005.1699 0.6172734 0.071135775 1.1634109 -0.217971994 1.4525187
## 2005.1726 0.6384796 0.091868234 1.1850910 -0.197490364 1.4744496
## 2005.1753 0.7241334 0.177048560 1.2712182 -0.112560650 1.5608274
## 2005.1781 0.6788397 0.131281831 1.2263975 -0.158577775 1.5162571
## 2005.1808 0.8006346 0.252604149 1.3486650 -0.037505635 1.6387748
## 2005.1836 0.6075687 0.059066091 1.1560713 -0.231293657 1.4464311
## 2005.1863 0.4655810 -0.083393446 1.0145554 -0.374002943 1.3051649
## 2005.1890 0.3681486 -0.181297219 0.9175944 -0.472156249 1.2084534
## 2005.1918 0.3647278 -0.185189006 0.9146445 -0.476297357 1.2057529
## 2005.1945 0.6882615 0.137874126 1.2386488 -0.153483331 1.5300063
## 2005.1973 0.7578975 0.207040025 1.3087550 -0.084566326 1.6003614
## 2005.2000 0.6855802 0.134252895 1.2369075 -0.157602138 1.5287625
## 2005.2027 0.7235325 0.171735799 1.2753291 -0.120367704 1.5674326
## 2005.2055 0.6914548 0.139189207 1.2437205 -0.153162556 1.5360722
## 2005.2082 0.6563413 0.103607057 1.2090755 -0.188992754 1.5016753
## 2005.2110 0.5914371 0.038234682 1.1446394 -0.254612967 1.4374871
## 2005.2137 0.6393040 0.085633811 1.1929741 -0.207461466 1.4860694
## 2005.2164 0.4569210 -0.097216496 1.0110586 -0.390559193 1.3044013
## 2005.2192 0.5409456 -0.013658980 1.0955501 -0.307248888 1.3891400
## 2005.2219 0.6058790 0.050807872 1.1609501 -0.243029039 1.4547871
## 2005.2247 0.6733852 0.117847857 1.2289225 -0.176235850 1.5230063
## 2005.2274 0.5141911 -0.041812037 1.0701943 -0.336142332 1.3645246
## 2005.2301 0.4402605 -0.116208089 0.9967291 -0.410784767 1.2913058
## 2005.2329 0.6333339 0.076400287 1.1902675 -0.218422567 1.4850904
## 2005.2356 0.6125622 0.055163887 1.1699604 -0.239904938 1.4650293
## 2005.2384 0.5123836 -0.045478977 1.0702461 -0.340793568 1.3655607
## 2005.2411 0.7413918 0.183065332 1.2997182 -0.112494820 1.5952783
## 2005.2438 0.7967543 0.237964435 1.3555443 -0.057841075 1.6513498
## 2005.2466 0.9064421 0.347189084 1.4656951 0.051138419 1.7617458
## 2005.2493 0.8315019 0.271786201 1.3912177 -0.024509415 1.6875133
## 2005.2521 0.5809850 0.020806962 1.1411631 -0.275733404 1.4377035
## 2005.2548 0.6727809 0.112140868 1.2334210 -0.184644045 1.5302059
## 2005.2575 0.6503021 0.089200480 1.2114037 -0.207828780 1.5084330
## 2005.2603 0.4831357 -0.078427116 1.0446985 -0.375700521 1.3419719
## 2005.2630 0.5194179 -0.042605712 1.0814416 -0.340123062 1.3789589
## 2005.2658 0.5233246 -0.039159526 1.0858087 -0.336920621 1.3835698
## 2005.2685 0.6681129 0.105168706 1.2310570 -0.192835935 1.5290617
## 2005.2712 0.5843268 0.020922945 1.1477307 -0.277325043 1.4459787
## 2005.2740 0.4994809 -0.064382305 1.0633441 -0.362873441 1.3618352
## 2005.2767 0.5626058 -0.001716366 1.1269279 -0.300450453 1.4256620
## 2005.2795 0.5115828 -0.053197891 1.0763635 -0.352174731 1.3753403
## 2005.2822 0.6927907 0.127551843 1.2580296 -0.171667553 1.5572490
## 2005.2849 0.7145352 0.148838435 1.2802319 -0.150623321 1.5796936
## 2005.2877 0.6984662 0.132312040 1.2646204 -0.167391879 1.5643243
## 2005.2904 0.4925580 -0.074053320 1.0591692 -0.373999208 1.3591151
## 2005.2932 0.5414262 -0.025641786 1.1084942 -0.325829448 1.4086819
## 2005.2959 0.5121307 -0.055393617 1.0796551 -0.355822856 1.3800843
## 2005.2986 0.6199850 0.052004643 1.1879653 -0.248665982 1.4886359
## 2005.3014 0.7866214 0.218185467 1.3550574 -0.082726348 1.6559692
## 2005.3041 0.7681789 0.199287647 1.3370701 -0.101865166 1.6382229
## 2005.3068 0.6904692 0.121123056 1.2598153 -0.180270562 1.5612089
## 2005.3096 0.5434475 -0.026353125 1.1132481 -0.327987356 1.4148824
## 2005.3123 0.7219339 0.151679105 1.2921887 -0.150195547 1.5940633
## 2005.3151 0.6435051 0.072796494 1.2142137 -0.229318387 1.5163286
## 2005.3178 0.7618530 0.190690928 1.3330150 -0.111663992 1.6353699
## 2005.3205 0.7427656 0.171150452 1.3143807 -0.131444317 1.6169755
## 2005.3233 0.7982716 0.226203793 1.3703395 -0.076630634 1.6731739
## 2005.3260 0.7701508 0.197630566 1.3426710 -0.105443330 1.6457449
## 2005.3288 0.8141442 0.241172011 1.3871165 -0.062141166 1.6904296
## 2005.3315 0.5940443 0.020620384 1.1674681 -0.282931884 1.4710204
## 2005.3342 0.4057537 -0.168121511 0.9796289 -0.471912681 1.2834200
## 2005.3370 0.6349567 0.060630580 1.2092828 -0.243399306 1.5133127
## 2005.3397 0.6912215 0.116444826 1.2659983 -0.187823588 1.5702667
## 2005.3425 0.7004929 0.125265951 1.2757199 -0.179240804 1.5802266
## 2005.3452 0.5643836 -0.011293226 1.1400605 -0.316038136 1.4448054
## 2005.3479 0.5971756 0.021049223 1.1733020 -0.283933656 1.4782848
## 2005.3507 0.6025342 0.025958608 1.1791097 -0.279262054 1.4843304
## 2005.3534 0.6614977 0.084473335 1.2385221 -0.220984925 1.5439804
## 2005.3562 0.5065863 -0.070886604 1.0840591 -0.376582278 1.3897548
## 2005.3589 0.4612126 -0.116708390 1.0391336 -0.422641293 1.3450665
## 2005.3616 0.7513036 0.172934791 1.3296724 -0.133235158 1.6358423
## 2005.3644 0.6670635 0.088247257 1.2458797 -0.218159553 1.5522866
## 2005.3671 0.6735360 0.094272701 1.2527994 -0.212370789 1.5594429
## 2005.3699 0.7291713 0.149461232 1.3088814 -0.157418754 1.6157614
## 2005.3726 0.6910850 0.110928541 1.2712415 -0.196187760 1.5783578
## 2005.3753 0.7352996 0.154697080 1.3159022 -0.152655353 1.6232546
## 2005.3781 0.8032623 0.222213959 1.3843105 -0.085374426 1.6918989
## 2005.3808 0.7303742 0.148880502 1.3118678 -0.158943654 1.6196920
## 2005.3836 0.6088465 0.026907814 1.1907852 -0.281151932 1.4988450
## 2005.3863 0.7944344 0.212051029 1.3768179 -0.096244127 1.6851130
## 2005.3890 0.7295727 0.146744964 1.3124005 -0.161785423 1.6209309
## 2005.3918 0.7368402 0.153568413 1.3201120 -0.155197025 1.6288774
## 2005.3945 0.8427149 0.258999429 1.4264304 -0.050000882 1.7354307
## 2005.3973 0.8203734 0.236214590 1.4045322 -0.073020415 1.7137673
## 2005.4000 0.8536087 0.269006837 1.4382105 -0.040462684 1.7476800
## 2005.4027 0.8503690 0.265324478 1.4354135 -0.044379381 1.7451174
## 2005.4055 0.8417291 0.256242219 1.4272159 -0.053695802 1.7371540
## 2005.4082 0.8615636 0.275634692 1.4474924 -0.034537314 1.7576644
## 2005.4110 0.8056894 0.219318861 1.3920599 -0.091086953 1.7024658
## 2005.4137 0.6987824 0.111970550 1.2855943 -0.198668896 1.5962338
## 2005.4164 0.7335847 0.146331768 1.3208376 -0.164541135 1.6317105
## 2005.4192 0.8435064 0.255812811 1.4312000 -0.055293373 1.7423061
## 2005.4219 0.7866572 0.198523247 1.3747911 -0.112816044 1.6861304
## 2005.4247 0.9348751 0.346301140 1.5234490 0.034728916 1.8350212
## 2005.4274 0.8856140 0.296600340 1.4746276 -0.015204642 1.7864326
## 2005.4301 0.8839949 0.294541952 1.4734479 -0.017495614 1.7854855
## 2005.4329 0.8187265 0.228834495 1.4086186 -0.083435483 1.7208885
## 2005.4356 0.8088582 0.218527474 1.3991890 -0.093974742 1.7116912
## 2005.4384 0.7660536 0.175284480 1.3568227 -0.137449803 1.6695570
## 2005.4411 0.8003651 0.209157931 1.3915723 -0.103808245 1.7045385
## 2005.4438 0.7534894 0.161844510 1.3451343 -0.151353389 1.6583322
## 2005.4466 0.8263503 0.234267949 1.4184326 -0.079161501 1.7318620
## 2005.4493 0.8239641 0.231444688 1.4164835 -0.082216142 1.7301443
## 2005.4521 0.7992179 0.206261745 1.3921741 -0.107630295 1.7060661
## 2005.4548 0.7931283 0.199735710 1.3865210 -0.114387369 1.7006440
## 2005.4575 0.7532842 0.159455454 1.3471129 -0.154898495 1.6614669
## 2005.4603 0.7992506 0.204986094 1.3935152 -0.109598554 1.7080998
## 2005.4630 0.7382550 0.143554935 1.3329550 -0.171260245 1.6477702
## 2005.4658 0.6878402 0.092704962 1.2829754 -0.222340580 1.5980209
## 2005.4685 0.8700466 0.274476513 1.4656166 -0.040799223 1.7808923
## 2005.4712 0.8488557 0.252851078 1.4448602 -0.062654684 1.7603660
## 2005.4740 0.7790035 0.182564711 1.3754423 -0.133170910 1.6911779
## 2005.4767 0.8413452 0.244472480 1.4382178 -0.071492832 1.7541832
## 2005.4795 0.7740973 0.176791012 1.3714035 -0.139403825 1.6875984
## 2005.4822 0.7427011 0.144961599 1.3404407 -0.171462596 1.6568649
## 2005.4849 0.8324691 0.234296580 1.4306416 -0.082356807 1.7472949
## 2005.4877 0.8642048 0.265599683 1.4628099 -0.051282730 1.7796923
## 2005.4904 0.7045009 0.105463474 1.3035384 -0.211647800 1.6206497
## 2005.4932 0.6450355 0.045565994 1.2445049 -0.271773975 1.5618449
## 2005.4959 0.7268628 0.126961652 1.3267640 -0.190606848 1.6443325
## 2005.4986 0.7159586 0.115626036 1.3162912 -0.202170830 1.6340880
## 2005.5014 0.7945505 0.193786820 1.3953141 -0.124238249 1.7133392
## 2005.5041 0.7477166 0.146522155 1.3489110 -0.171730953 1.6671641
## 2005.5068 0.7089673 0.107342378 1.3105922 -0.211138606 1.6290732
## 2005.5096 0.7641209 0.162065851 1.3661760 -0.156642845 1.6848847
## 2005.5123 0.7028242 0.100339334 1.3053092 -0.218596912 1.6242454
## 2005.5151 0.7457759 0.142861423 1.3486903 -0.176302211 1.6678540
## 2005.5178 0.7400395 0.136695818 1.3433832 -0.182695043 1.6627741
## 2005.5205 0.7821120 0.178339404 1.3858847 -0.141278521 1.7055026
## 2005.5233 0.8162387 0.212037400 1.4204399 -0.107807429 1.7402848
## 2005.5260 0.8415881 0.236958509 1.4462177 -0.083113062 1.7662893
## 2005.5288 0.8292412 0.224183622 1.4342988 -0.096114530 1.7545970
## 2005.5315 0.8331482 0.227662853 1.4386335 -0.092861722 1.7591581
## 2005.5342 0.7926687 0.186755929 1.3985814 -0.133994907 1.7193323
## 2005.5370 0.7920329 0.185692989 1.3983727 -0.135283950 1.7193497
## 2005.5397 0.7814203 0.174653646 1.3881870 -0.146549237 1.7093899
## 2005.5425 0.7803950 0.173201792 1.3875882 -0.148226875 1.7090169
## 2005.5452 0.7513843 0.143764907 1.3590038 -0.177889386 1.6806580
## 2005.5479 0.8256343 0.217588972 1.4336797 -0.104290789 1.7555594
## 2005.5507 0.8094534 0.200982397 1.4179243 -0.121122674 1.7400294
## 2005.5534 0.7731100 0.164213730 1.3820063 -0.158116493 1.7043365
## 2005.5562 0.7743631 0.165041830 1.3836845 -0.157513388 1.7062397
## 2005.5589 0.8138349 0.204088883 1.4235810 -0.118691174 1.7463610
## 2005.5616 0.8141966 0.204026167 1.4243671 -0.118978572 1.7473719
## 2005.5644 0.7456027 0.135008056 1.3561973 -0.188221209 1.6794266
## 2005.5671 0.8361732 0.225154749 1.4471917 -0.098298885 1.7706453
## 2005.5699 0.8072868 0.195844765 1.4187288 -0.127833084 1.7424066
## 2005.5726 0.7594244 0.147559150 1.3712897 -0.176342758 1.6951916
## 2005.5753 0.7964734 0.184185187 1.4087617 -0.139940626 1.7328875
## 2005.5781 0.8088478 0.196136897 1.4215587 -0.128212665 1.7459083
## 2005.5808 0.7317502 0.118616926 1.3448835 -0.205956232 1.6694567
## 2005.5836 0.8617991 0.248243671 1.4753544 -0.076552928 1.8001510
## 2005.5863 0.8489999 0.235022682 1.4629770 -0.089997206 1.7879969
## 2005.5890 0.7503520 0.135953271 1.3647507 -0.189289751 1.6899937
## 2005.5918 0.7935974 0.178777446 1.4084173 -0.146688558 1.7338833
## 2005.5945 0.6962466 0.081005718 1.3114874 -0.244683115 1.6371763
## 2005.5973 0.7197816 0.104120103 1.3354431 -0.221791407 1.6613546
## 2005.6000 0.7477828 0.131700983 1.3638647 -0.194433051 1.6899987
## 2005.6027 0.7706745 0.154172584 1.3871764 -0.172183823 1.7135328
## 2005.6055 0.7626004 0.145678638 1.3795221 -0.180899991 1.7061007
## 2005.6082 0.8835149 0.266173668 1.5008561 -0.060627032 1.8276568
## 2005.6110 0.8246786 0.206918176 1.4424390 -0.120104443 1.7694617
## 2005.6137 0.8283721 0.210192774 1.4465515 -0.117051614 1.7737959
## 2005.6164 0.7917123 0.173114247 1.4103103 -0.154351760 1.7377763
## 2005.6192 0.7649834 0.145966997 1.3839998 -0.181720479 1.7116872
## 2005.6219 0.6603092 0.040874777 1.2797437 -0.287034018 1.6076525
## 2005.6247 0.7787516 0.158899313 1.3986038 -0.169230652 1.7267338
## 2005.6274 0.8079520 0.187682242 1.4282218 -0.140668745 1.7565728
## 2005.6301 0.7304504 0.109763375 1.3511374 -0.218808484 1.6797093
## 2005.6329 0.8681154 0.247011426 1.4892194 -0.081781158 1.8180120
## 2005.6356 0.9154196 0.293898930 1.5369402 -0.035114229 1.8659534
## 2005.6384 0.8228060 0.200868992 1.4447431 -0.128364596 1.7739767
## 2005.6411 0.8252123 0.202859132 1.4475655 -0.126594736 1.7770193
## 2005.6438 0.7093002 0.086531228 1.3320693 -0.243142774 1.6617433
## 2005.6466 0.7411020 0.117917432 1.3642866 -0.211976558 1.6941806
## 2005.6493 0.8037303 0.180130409 1.4273301 -0.149983420 1.7574440
## 2005.6521 0.7398815 0.115866661 1.3638964 -0.214466862 1.6942299
## 2005.6548 0.8760843 0.251654695 1.5005139 -0.078898376 1.8310670
## 2005.6575 0.7259528 0.101108679 1.3507968 -0.229663794 1.6815693
## 2005.6603 0.7167740 0.091515784 1.3420323 -0.239475946 1.6730240
## 2005.6630 0.8248458 0.199173612 1.4505180 -0.132037229 1.7817288
## 2005.6658 0.9069702 0.280884413 1.5330560 -0.050545395 1.8644858
## 2005.6685 0.7036291 0.077129877 1.3301282 -0.254518753 1.6617769
## 2005.6712 0.7102652 0.083352957 1.3371775 -0.248514351 1.6690448
## 2005.6740 0.7709246 0.143599494 1.3982497 -0.188486347 1.7303355
## 2005.6767 0.7111675 0.083429885 1.3389052 -0.248874347 1.6712094
## 2005.6795 0.7054254 0.077275450 1.3335753 -0.255247029 1.6660978
## 2005.6822 0.8331998 0.204637873 1.4617617 -0.128102709 1.7945023
## 2005.6849 0.7490313 0.120057664 1.3780050 -0.212900878 1.7109635
## 2005.6877 0.6214483 -0.007936875 1.2508334 -0.341113235 1.5840097
## 2005.6904 0.7269742 0.097177866 1.3567705 -0.236216171 1.6901646
## 2005.6932 0.6699687 0.039761461 1.3001760 -0.293850110 1.6337875
## 2005.6959 0.5388099 -0.091807976 1.1694279 -0.425636938 1.5032568
## 2005.6986 0.7514977 0.120469364 1.3825260 -0.213576849 1.7165722
## 2005.7014 0.5616630 -0.069775455 1.1931014 -0.404038777 1.5273648
## 2005.7041 0.6117862 -0.020062120 1.2436345 -0.354542411 1.5781148
## 2005.7068 0.6306124 -0.001645466 1.2628703 -0.336342584 1.5975675
## 2005.7096 0.6892057 0.056538421 1.3218729 -0.278375385 1.6567867
## 2005.7123 0.6998181 0.066741798 1.3328944 -0.268388555 1.6680248
## 2005.7151 0.6083076 -0.025177495 1.2417927 -0.360524255 1.5771395
## 2005.7178 0.6170926 -0.016801074 1.2509862 -0.352364102 1.5865493
## 2005.7205 0.5743151 -0.059986815 1.2086170 -0.395765971 1.5443962
## 2005.7233 0.7745075 0.139797526 1.4092174 -0.196197620 1.7452126
## 2005.7260 0.7957426 0.160624907 1.4308603 -0.175586089 1.7670713
## 2005.7288 0.7035257 0.068000559 1.3390509 -0.268426150 1.6754776
## 2005.7315 0.5865873 -0.049345138 1.2225197 -0.385987421 1.5591620
## 2005.7342 0.6275986 -0.008740748 1.2639380 -0.345598468 1.6007957
## 2005.7370 0.5183230 -0.118423104 1.1550691 -0.455496122 1.4921421
## 2005.7397 0.5650978 -0.072054758 1.2022503 -0.409342936 1.5395385
## 2005.7425 0.7053450 0.067786275 1.3429037 -0.269716927 1.6804069
## 2005.7452 0.6431620 0.005197381 1.2811267 -0.332520709 1.6188448
## 2005.7479 0.6536181 0.015247796 1.2919885 -0.322685044 1.6299213
## 2005.7507 0.6844069 0.045631167 1.3231827 -0.292516286 1.6613301
## 2005.7534 0.5749306 -0.064250285 1.2141115 -0.402612216 1.5524735
## 2005.7562 0.8002850 0.160699170 1.4398708 -0.177877103 1.7784471
## 2005.7589 0.6988698 0.058879337 1.3388602 -0.279911143 1.6776507
## 2005.7616 0.7148912 0.074496334 1.3552860 -0.264508216 1.6942906
## 2005.7644 0.6205327 -0.020266311 1.2613316 -0.359484798 1.6005501
## 2005.7671 0.5049602 -0.136242623 1.1461631 -0.475674911 1.4855954
## 2005.7699 0.3970287 -0.244577772 1.0386352 -0.584223726 1.3782811
## 2005.7726 0.7000421 0.058032297 1.3420520 -0.281827189 1.6819115
## 2005.7753 0.7136026 0.071189665 1.3560156 -0.268883219 1.6960885
## 2005.7781 0.5398700 -0.102945876 1.1826858 -0.443232024 1.5229719
## 2005.7808 0.7454226 0.102204126 1.3886410 -0.238295152 1.7291403
## 2005.7836 0.5409381 -0.102682720 1.1845589 -0.443394996 1.5252712
## 2005.7863 0.5875822 -0.056440712 1.2316051 -0.397365852 1.5725303
## 2005.7890 0.3789150 -0.265509806 1.0233398 -0.606647678 1.3644776
## 2005.7918 0.3720228 -0.272803545 1.0168492 -0.614154016 1.3581997
## 2005.7945 0.3954460 -0.249781757 1.0406737 -0.591344694 1.3822367
## 2005.7973 0.5451753 -0.100453564 1.1908041 -0.442228835 1.5325794
## 2005.8000 0.6780347 0.032004939 1.3240644 -0.309982535 1.6660518
## 2005.8027 0.6980870 0.051656716 1.3445174 -0.290542829 1.6867169
## 2005.8055 0.5978873 -0.048943416 1.2447180 -0.391354901 1.5871295
## 2005.8082 0.5589633 -0.088267535 1.2061941 -0.430890828 1.5488174
## 2005.8110 0.4477275 -0.199903196 1.0953582 -0.542738167 1.4381931
## 2005.8137 0.7220120 0.073981662 1.3700423 -0.269064856 1.7130888
## 2005.8164 0.5066179 -0.141811822 1.1550475 -0.485069757 1.4983055
## 2005.8192 0.6161771 -0.032651680 1.2650059 -0.376120901 1.6084751
## 2005.8219 0.4966312 -0.152596513 1.1458589 -0.496276890 1.4895392
## 2005.8247 0.6021744 -0.047451891 1.2518008 -0.391343296 1.5956922
## 2005.8274 0.5427273 -0.107297424 1.1927520 -0.451399727 1.5368543
## 2005.8301 0.7179324 0.067509499 1.3683552 -0.276803571 1.7126683
## 2005.8329 0.6736324 0.022811617 1.3244532 -0.321712093 1.6689769
## 2005.8356 0.4342586 -0.216959837 1.0854771 -0.561694058 1.4302113
## 2005.8384 0.3760001 -0.275615794 1.0276159 -0.620560397 1.3725605
## 2005.8411 0.6053154 -0.046697617 1.2573285 -0.391852474 1.6024833
## 2005.8438 0.6804294 0.028019451 1.3328394 -0.317345533 1.6782044
## 2005.8466 0.5143903 -0.138416345 1.1671970 -0.483991327 1.5127720
## 2005.8493 0.5897788 -0.063424331 1.2429819 -0.409209183 1.5887668
## 2005.8521 0.3820814 -0.271517907 1.0356808 -0.617512503 1.3816754
## 2005.8548 0.5320945 -0.121900796 1.1860899 -0.468105008 1.5322941
## 2005.8575 0.5222711 -0.132119946 1.1766622 -0.478533648 1.5230759
## 2005.8603 0.7177437 0.062957124 1.3725302 -0.283665941 1.7191533
## 2005.8630 0.8597176 0.204535824 1.5148995 -0.142296477 1.8617318
## 2005.8658 0.6072848 -0.048291998 1.2628617 -0.395333410 1.6099031
## 2005.8685 0.5255507 -0.130420929 1.1815223 -0.477671325 1.5287727
## 2005.8712 0.5310275 -0.125338689 1.1873936 -0.472797945 1.5348529
## 2005.8740 0.5683224 -0.088438066 1.2250829 -0.436106054 1.5727508
## 2005.8767 0.8134740 0.156319482 1.4706285 -0.191557114 1.8185051
## 2005.8795 0.6767441 0.019195750 1.3342925 -0.328889330 1.6823776
## 2005.8822 0.5357548 -0.122187174 1.1936968 -0.470480612 1.5419902
## 2005.8849 0.6448286 -0.013506750 1.3031639 -0.362008421 1.6516656
## 2005.8877 0.6667075 0.007979049 1.3254360 -0.340730732 1.6741457
## 2005.8904 0.5887509 -0.070370464 1.2478722 -0.419288230 1.5967900
## 2005.8932 0.5930738 -0.066440252 1.2525878 -0.415565880 1.6017134
## 2005.8959 0.6372996 -0.022606831 1.2972060 -0.371940196 1.6465394
## 2005.8986 0.6209683 -0.039330280 1.2812670 -0.388871259 1.6308080
## 2005.9014 0.5032821 -0.157408487 1.1639727 -0.507156957 1.5137212
## 2005.9041 0.5941201 -0.066962202 1.2552024 -0.416918040 1.6051583
## 2005.9068 0.5290517 -0.132422120 1.1905255 -0.482585203 1.5406886
## 2005.9096 0.5314034 -0.130461626 1.1932685 -0.480831832 1.5436387
## 2005.9123 0.7038493 0.041593197 1.3661054 -0.308984009 1.7166826
## 2005.9151 0.9054951 0.242848177 1.5681420 -0.107935907 1.9189261
## 2005.9178 0.7163707 0.053333257 1.3794082 -0.297657583 1.7303991
## 2005.9205 0.5719845 -0.091443308 1.2354123 -0.442640782 1.5866098
## 2005.9233 0.6209071 -0.042910865 1.2847250 -0.394314852 1.6361290
## 2005.9260 0.5314784 -0.132729391 1.1956862 -0.484339769 1.5472966
## 2005.9288 0.4856011 -0.178996361 1.1501986 -0.530813010 1.5020152
## 2005.9315 0.5517062 -0.113280705 1.2166931 -0.465303504 1.5687159
## 2005.9342 0.2449924 -0.420383736 0.9103685 -0.772612563 1.2625973
## 2005.9370 0.5088668 -0.156898255 1.1746319 -0.509332991 1.5270666
## 2005.9397 0.6630588 -0.003094989 1.3292126 -0.355735513 1.6818532
## 2005.9425 0.6137802 -0.052762173 1.2803225 -0.405608366 1.6331687
## 2005.9452 0.5375032 -0.129427369 1.2044339 -0.482479110 1.5574856
## 2005.9479 0.5150377 -0.152281017 1.1823563 -0.505538186 1.5356135
## 2005.9507 0.6270537 -0.040652785 1.2947602 -0.394115264 1.6482227
## 2005.9534 0.5061101 -0.161984060 1.1742042 -0.515651729 1.5278719
## 2005.9562 0.5704559 -0.098025603 1.2389374 -0.451898344 1.5928102
## 2005.9589 0.4453888 -0.223479882 1.1142575 -0.577557575 1.4683352
## 2005.9616 0.4662459 -0.203009714 1.1355015 -0.557292242 1.4897841
## 2005.9644 0.6087059 -0.060936462 1.2783482 -0.415423705 1.6328355
## 2005.9671 0.6229421 -0.047086782 1.2929709 -0.401778623 1.6476627
## 2005.9699 0.4400719 -0.230343172 1.1104870 -0.585239492 1.4653834
## 2005.9726 0.6059110 -0.064890166 1.2767121 -0.419990847 1.6318128
## 2005.9753 0.6360319 -0.035155050 1.3072189 -0.390459976 1.6625238
## 2005.9781 0.5470015 -0.124571088 1.2185741 -0.480080140 1.5740831
## 2005.9808 0.5174789 -0.154479105 1.1894368 -0.510192168 1.5451499
## 2005.9836 0.6443095 -0.028033598 1.3166527 -0.383950553 1.6725696
## 2005.9863 0.5288986 -0.143829435 1.2016267 -0.499950166 1.5577474
## 2005.9890 0.5947417 -0.078371062 1.2678545 -0.434695452 1.6241789
## 2005.9918 0.3032528 -0.370244488 0.9767501 -0.726772422 1.3332780
## 2005.9945 0.5454123 -0.128469233 1.2192939 -0.485200594 1.5760253
## 2005.9973 0.5047455 -0.169520128 1.1790112 -0.526454800 1.5359458
## 2006.0000 0.5453453 -0.129304172 1.2199948 -0.486442040 1.5771327
## 2006.0027 0.7679888 0.092955681 1.4430219 -0.264385266 1.8003629
## 2006.0055 0.5411754 -0.134241100 1.2165920 -0.491785011 1.5741359##NOTE: AIC = 10212.74, BIC = 10229.82 , RMSE = 0.2188444 Also, the headline of the plot below contains ETS(A,N,N) showing that the automated model characterized error of the “tsWSR_PK” SERIES as Additative (A), trend as None (A) and seasonality as None (N) which is equivalent to simple exponential model(ses) with only alpha parameter i.e level.
#Model 2 : ARIMA Model
#2.1 Auto Arima model without sesonality:
set.seed(301)
model_Var5 <- auto.arima(train4, seasonal = FALSE)
summary(model_Var5)## Series: train4
## ARIMA(3,0,1) with non-zero mean
##
## Coefficients:
## ar1 ar2 ar3 ma1 mean
## 1.3782 -0.5089 0.1162 -0.9370 0.5683
## s.e. 0.0253 0.0348 0.0218 0.0145 0.0209
##
## sigma^2 estimated as 0.05254: log likelihood=121.04
## AIC=-230.07 AICc=-230.03 BIC=-195.91
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set 0.0003031604 0.2289515 0.1832716 -71.02974 94.35383 0.6576897
## ACF1
## Training set 0.0003856439##NOTE: AIC = -230.07 , BIC = -195.91 , RMSE = 0.2289515
tsdisplay(residuals(model_Var5), lag.max = 45, main = '(1,1,1) Model Residuals')
#2.2 Auto Arima model with sesonality:
set.seed(301)
model2_Var5 <- auto.arima(train4, seasonal= TRUE)
summary(model2_Var5)## Series: train4
## ARIMA(5,0,2) with non-zero mean
##
## Coefficients:
## ar1 ar2 ar3 ar4 ar5 ma1 ma2 mean
## 0.4184 0.8105 -0.3610 0.0955 0.0078 0.0255 -0.9012 0.5693
## s.e. 0.0330 0.0375 0.0305 0.0243 0.0227 0.0253 0.0245 0.0208
##
## sigma^2 estimated as 0.0525: log likelihood=123.35
## AIC=-228.69 AICc=-228.61 BIC=-177.46
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set 7.119779e-05 0.2287086 0.1830377 -71.09868 94.38878 0.6568503
## ACF1
## Training set -0.0001554728##NOTE: AIC = -228.69 , BIC = -177.46 , RMSE = 0.2287086
tsdisplay(residuals(model2_Var5), lag.max = 20, main = 'Seasonal Model Residuals')
NOTE: Above Graphs does not shows serious lags
#Plotting forecast for each model
par(mfrow = c(2,2))
fit_auto_train_Var5 %>% forecast(h=341) %>% autoplot() 
model2_Var5 %>% forecast(h=341) %>% autoplot() 
model_Var5 %>% forecast(h=341) %>% autoplot() 
Plot and comment on the residuals of the fitted data for both models in the same plot.
Residual Plot - to confirm no problem with this model
par(mfrow= c(2,2))
hist(fit_auto_train_Var5$residuals,col = 'red',xlab = 'Error',main = 'Histogram Of Residuals',freq= FALSE)
lines(density(fit_auto_train_Var5$residuals))
hist(model_Var5$residuals,col = 'red',xlab = 'Error',main = 'Histogram Of Residuals',freq= FALSE)
lines(density(model_Var5$residuals))
hist(model2_Var5$residuals,col = 'red',xlab = 'Error',main = 'Histogram Of Residuals',freq= FALSE)
lines(density(model2_Var5$residuals))
OBSERVATION:
The residuals for each model are normally distributed, which shows the good fit of the models. It is normally distrbuted
Testing the autocorrelation and partial autocorrelation of the residuals (using the plots and Ljung-Box Q statistic) up to an appropriate lag *
- ACF & PACF Plots
par(mfrow = c(3,2))
acf(fit_auto_train_Var5$residuals, main = 'Correlogram')
pacf(fit_auto_train_Var5$residuals, main = 'Partial Corelogram')
acf(model_Var5$residuals, main = 'Correlogram')
pacf(model_Var5$residuals, main = 'Partial Corelogram')
acf(model2_Var5$residuals, main = 'Correlogram')
pacf(model2_Var5$residuals, main = 'Partial Corelogram')
NOTE:
1. Residuals are the difference between actaual and fitted values
2. These blue lines are signficance bounds
3. This graph shows us the autocorelations for insample forecast errors
4. Do not exceed these significance bounds for lags 1 to end
#Ljunx-Box Test to check the autocorelations of the residuals
HO: No serial correlation upto 20 lags (does not exhibit lack of fit of the model)
Ha: Serial corelation is present (the model exhibits lack of fit)
We reject the null hypothesis, if p value is less than 0.05. This test is generally done for ARIMA models
Box.test(model_Var5$residuals, lag =20, type = 'Ljung-Box')##
## Box-Ljung test
##
## data: model_Var5$residuals
## X-squared = 10.265, df = 20, p-value = 0.9631Box.test(model2_Var5$residuals, lag =20, type = 'Ljung-Box')##
## Box-Ljung test
##
## data: model2_Var5$residuals
## X-squared = 8.4094, df = 20, p-value = 0.9888OBSERVATIONS: For above performed Ljunx-Box Test on both arima models, we can say that p-value is more than significance level 0.05, then there is not a statistical significance.
We conclude that there is a liitle evidence of non-zero auto-corelations in the insample forecast errors at lags 1 to 20.
So we fail to rejects the null hypothesis. Hence, we conclude that there is no serial auto corelation present between lags. Hence, both model seems to be good fit.
Validating The Model by testing the model performance with Holdout set
Here, choosing RMSE as evaluation parameter. The lower RMSE indicates a more accurate forecast.
Below, is the comparison of model. We are fitting the model to test set which is the holdout set. And checking the accuracy using RMSE(Root mean square error) evaluation parameter.
accuracy(forecast(fit_auto_train_Var5), test4) ["Test set", "RMSE"]## [1] 0.2604829#o/p - 0.2604829accuracy(forecast(model2_Var5), test4) ["Test set", "RMSE"]## [1] 0.248869#o/p - 0.248869accuracy(forecast(model_Var5), test4) ["Test set", "RMSE"]## [1] 0.2489681#O/P - 0.2489681NOTE:-
Here, the RMSE value is less of ARIMA models compared to exponential model.
The minimum RMSE is of model2_Var5.
COMMENT ON BEST MODEL AND ITS PARAMETERS
We observed the best model to be ARIMA model i.e.“model2_Var5”.
summary(model2_Var5)## Series: train4
## ARIMA(5,0,2) with non-zero mean
##
## Coefficients:
## ar1 ar2 ar3 ar4 ar5 ma1 ma2 mean
## 0.4184 0.8105 -0.3610 0.0955 0.0078 0.0255 -0.9012 0.5693
## s.e. 0.0330 0.0375 0.0305 0.0243 0.0227 0.0253 0.0245 0.0208
##
## sigma^2 estimated as 0.0525: log likelihood=123.35
## AIC=-228.69 AICc=-228.61 BIC=-177.46
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set 7.119779e-05 0.2287086 0.1830377 -71.09868 94.38878 0.6568503
## ACF1
## Training set -0.0001554728Best Model is ARIMA (5,0,2) ,which means
p = 5
d = 0
q = 2
For the best model, 5 members of lag are used as a predictor.
As the series was stationary so members of differences needed for stationarity is 0.
2 are the number of lagged forecasts errors used in the prediction equation.
AIC = 6173.8, RMSE = 0.9795425 which is minimum as compared to other models.
6. Forecasting on Geopotential height at 850 hpa, it is about the same as height at low altitude (HT85)
#Checking the attributes of time series
attributes(tsHT85)## $tsp
## [1] 1998.00 2004.94 365.00
##
## $class
## [1] "ts"#Plotting the series
plot(tsHT85, main = "Geopotential height at 850 hpa (tsHT85)", col = "orange")
From the plot, we observes that there seems slight upward trend also seems to have seasonlity.
Checking the statistics and visualising the missing data in the series:
plotNA.distribution(tsHT85)
#data is missing at random
As we see here data is missing randomly, so locf and NOCB would seems the good technique to implement here.
#Impute the missing values with “na_locf” function of “imputeTS package” and visualise the imputed values in the time series
tsHT85.imp <- na_locf(tsHT85)
plotNA.imputations(tsHT85, tsHT85.imp)
#Decomposition Of Time Series
decomp5 <- decompose(tsHT85.imp)
plot(decomp5, col = "red")
OBSERVATIONS:
1)There seems to have trend.
2) It seems to have upward trend from 1998 to around year 2000 and from year 2003 to 2005.
3) Also, observes downward trend from year 2000 to 2003.
4) We observe some seasonality in the series. Seasonality describes cyclical effects due to the time of the year.
Let’s explore this seasonality pattern by plotting the decomp$seasonal components such that y-axis represents Seasonality Index and x-axis has month
#Plotting the decomposed series
plot(decomp5$seasonal[1:365], type ='b', xlab = 'Years', ylab = 'Seasonality Index', col = 'blue', las = 2, main = "SEASONAL DATA")
OBSERVATIONS:
There is increase in the height in mid of the year and a drop in height for starting and end months of a year and we could think the reason because of seasonal change.
Stationarity check of time series
We could check the stationarity of time series by ADF and KPSS Tests:
- Augmented Dickey- Fuller(ADF) t-statistic test for unit root
- Kwiatkowski-Phillips-Schmidt-Shin (KPSS) for level or trend stationarity
adf.test(tsHT85.imp)## Warning in adf.test(tsHT85.imp): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: tsHT85.imp
## Dickey-Fuller = -7.7214, Lag order = 13, p-value = 0.01
## alternative hypothesis: stationary#smaller p-value, it is stationary kpss.test(tsHT85.imp, null="Trend")## Warning in kpss.test(tsHT85.imp, null = "Trend"): p-value smaller than printed
## p-value##
## KPSS Test for Trend Stationarity
##
## data: tsHT85.imp
## KPSS Trend = 0.33086, Truncation lag parameter = 8, p-value = 0.01#smaller p-value, hence not stationaryNOTE: From the both tests results, it leads to CASE4, we could recheck by visualising it i.e. by plotting ACF. Second, we can check each for characteristics of stationarity by looking at the autocorrelation functions (ACF) of each signal. For a stationary signal, because we expect no dependence with time, we would expect the ACF to go to 0 for each time lag (τ). Lets visualize the signals and ACFs.
acf(tsHT85.imp,lag.max = length(tsHT85.imp),xlab = "lag #", ylab = 'ACF',main='Statiionary Check ')
NOTE: There are significant lags which lies outside the significance bound. Hence, series is not stationary.
Now, we will take the difference to make our data stationary.
It seems difference of 1 is sufficient to make the series stationary.
tsHT85.sta <- diff(tsHT85.imp, diff = 1)
acf(tsHT85.sta, lag.max = length(tsHT85.sta),xlab = "lag #", ylab = 'ACF',main='Statiionary Check ')
Hence, after differencing our series is now transformed to stationary time series.
#Visualising the stationary series
plot(tsHT85.sta, col = "red")
#CREATING MODELS AND FORECASTING: USING EXPONENTIAL SMOOTHING AND ARIMA TECHNIQUES FOR TIME SERIES FORECASTING
1.Train - Test Split of the data
train5 <- window(tsHT85.imp, end = c(2004, 3))
test5 <- window(tsHT85.imp, start = c(2004, 4))#Model 1 : Auto Exponential Smoothening Model
set.seed(301)
fit_auto_train_Var6 <- forecast(train5)
summary(fit_auto_train_Var6)##
## Forecast method: STL + ETS(A,N,N)
##
## Model Information:
## ETS(A,N,N)
##
## Call:
## ets(y = na.interp(x), model = etsmodel, allow.multiplicative.trend = allow.multiplicative.trend)
##
## Smoothing parameters:
## alpha = 0.9999
##
## Initial states:
## l = 1592.2734
##
## sigma: 21.4263
##
## AIC AICc BIC
## 30316.22 30316.23 30333.30
##
## Error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -0.0699278 21.41649 15.85792 -0.01493587 1.04192 0.4709139
## ACF1
## Training set 0.1682468
##
## Forecasts:
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 2004.0082 1455.408 1427.9487 1482.866 1413.4128 1497.402
## 2004.0110 1450.174 1411.3435 1489.005 1390.7878 1509.561
## 2004.0137 1449.436 1401.8788 1496.993 1376.7037 1522.168
## 2004.0164 1420.343 1365.4298 1475.257 1336.3603 1504.327
## 2004.0192 1405.574 1344.1787 1466.969 1311.6781 1499.469
## 2004.0219 1424.431 1357.1765 1491.686 1321.5741 1527.288
## 2004.0247 1436.933 1364.2896 1509.576 1325.8347 1548.031
## 2004.0274 1430.573 1352.9143 1508.232 1311.8044 1549.341
## 2004.0301 1420.404 1338.0347 1502.773 1294.4311 1546.377
## 2004.0329 1421.944 1335.1193 1508.769 1289.1571 1554.731
## 2004.0356 1433.895 1342.8330 1524.958 1294.6275 1573.163
## 2004.0384 1433.117 1338.0054 1528.229 1287.6564 1578.578
## 2004.0411 1417.577 1318.5817 1516.572 1266.1768 1568.977
## 2004.0438 1406.612 1303.8799 1509.344 1249.4968 1563.727
## 2004.0466 1404.724 1298.3866 1511.062 1242.0948 1567.354
## 2004.0493 1415.348 1305.5228 1525.173 1247.3848 1583.311
## 2004.0521 1434.186 1320.9813 1547.392 1261.0541 1607.319
## 2004.0548 1455.310 1338.8234 1571.798 1277.1589 1633.462
## 2004.0575 1444.418 1324.7394 1564.098 1261.3852 1627.452
## 2004.0603 1450.817 1328.0286 1573.605 1263.0285 1638.605
## 2004.0630 1445.513 1319.6932 1571.334 1253.0879 1637.939
## 2004.0658 1419.866 1291.0845 1548.647 1222.9119 1616.819
## 2004.0685 1412.971 1281.2959 1544.647 1211.5911 1614.352
## 2004.0712 1427.331 1292.8234 1561.838 1221.6195 1633.042
## 2004.0740 1429.448 1292.1668 1566.729 1219.4946 1639.401
## 2004.0767 1424.141 1284.1411 1564.141 1210.0297 1638.252
## 2004.0795 1439.794 1297.1269 1582.460 1221.6038 1657.983
## 2004.0822 1428.464 1283.1798 1573.749 1206.2708 1650.658
## 2004.0849 1397.517 1249.6609 1545.373 1171.3905 1623.644
## 2004.0877 1416.996 1266.6124 1567.380 1187.0040 1646.988
## 2004.0904 1424.781 1271.9114 1577.651 1190.9871 1658.575
## 2004.0932 1427.872 1272.5560 1583.187 1190.3368 1665.407
## 2004.0959 1429.397 1271.6729 1587.121 1188.1790 1670.615
## 2004.0986 1428.660 1268.5646 1588.756 1183.8150 1673.506
## 2004.1014 1435.094 1272.6612 1597.527 1186.6743 1683.514
## 2004.1041 1438.982 1274.2449 1603.719 1187.0383 1690.926
## 2004.1068 1443.297 1276.2878 1610.307 1187.8783 1698.716
## 2004.1096 1433.449 1264.1974 1602.700 1174.6012 1692.296
## 2004.1123 1414.543 1243.0788 1586.006 1152.3114 1676.774
## 2004.1151 1403.567 1229.9185 1577.215 1137.9947 1669.138
## 2004.1178 1405.912 1230.1064 1581.717 1137.0407 1674.783
## 2004.1205 1420.234 1242.2981 1598.171 1148.1043 1692.365
## 2004.1233 1432.160 1252.1178 1612.202 1156.8093 1707.511
## 2004.1260 1418.327 1236.2034 1600.451 1139.7930 1696.861
## 2004.1288 1413.408 1229.2262 1597.589 1131.7264 1695.089
## 2004.1315 1401.204 1214.9872 1587.421 1116.4099 1685.998
## 2004.1342 1393.419 1205.1886 1581.649 1105.5456 1681.292
## 2004.1370 1405.684 1215.4624 1595.906 1114.7650 1696.604
## 2004.1397 1434.896 1242.7032 1627.090 1140.9623 1728.830
## 2004.1425 1430.689 1236.5445 1624.833 1133.7706 1727.607
## 2004.1452 1422.273 1226.1972 1618.350 1122.4007 1722.146
## 2004.1479 1411.613 1213.6234 1609.602 1108.8142 1714.411
## 2004.1507 1393.133 1193.2494 1593.017 1087.4372 1698.829
## 2004.1534 1393.228 1191.4676 1594.989 1084.6619 1701.795
## 2004.1562 1394.356 1190.7353 1597.976 1082.9452 1705.766
## 2004.1589 1386.343 1180.8796 1591.806 1072.1140 1700.571
## 2004.1616 1403.492 1196.2025 1610.781 1086.4701 1720.514
## 2004.1644 1417.810 1208.7097 1626.909 1098.0189 1737.600
## 2004.1671 1385.675 1174.7798 1596.569 1063.1388 1708.210
## 2004.1699 1394.340 1181.6653 1607.014 1069.0822 1719.597
## 2004.1726 1413.050 1198.6109 1627.490 1085.0936 1741.007
## 2004.1753 1411.571 1195.3811 1627.761 1080.9370 1742.205
## 2004.1781 1389.549 1171.6223 1607.475 1056.2590 1722.839
## 2004.1808 1377.954 1158.3049 1597.603 1042.0296 1713.879
## 2004.1836 1392.794 1171.4356 1614.153 1054.2555 1731.333
## 2004.1863 1446.625 1223.5706 1669.680 1105.4925 1787.758
## 2004.1890 1456.179 1231.4403 1680.917 1112.4710 1799.886
## 2004.1918 1437.790 1211.3805 1664.199 1091.5267 1784.053
## 2004.1945 1433.818 1205.7502 1661.886 1085.0183 1782.618
## 2004.1973 1435.703 1205.9886 1665.418 1084.3850 1787.021
## 2004.2000 1428.783 1197.4338 1660.133 1074.9647 1782.602
## 2004.2027 1407.770 1174.7970 1640.743 1051.4685 1764.072
## 2004.2055 1381.732 1147.1462 1616.317 1022.9641 1740.499
## 2004.2082 1387.471 1151.2846 1623.658 1026.2549 1748.688
## 2004.2110 1396.179 1158.4017 1633.956 1032.5301 1759.828
## 2004.2137 1411.198 1171.8410 1650.555 1045.1329 1777.263
## 2004.2164 1403.995 1163.0686 1644.922 1035.5297 1772.461
## 2004.2192 1410.955 1168.4693 1653.442 1040.1049 1781.806
## 2004.2219 1438.958 1194.9225 1682.994 1065.7379 1812.178
## 2004.2247 1456.357 1210.7818 1701.932 1080.7821 1831.932
## 2004.2274 1456.336 1209.2304 1703.441 1078.4208 1834.251
## 2004.2301 1440.118 1191.4922 1688.744 1059.8775 1820.359
## 2004.2329 1416.225 1166.0880 1666.363 1033.6733 1798.778
## 2004.2356 1429.560 1177.9205 1681.200 1044.7105 1814.410
## 2004.2384 1436.662 1183.5293 1689.796 1049.5287 1823.796
## 2004.2411 1422.209 1167.5913 1676.827 1032.8048 1811.613
## 2004.2438 1427.304 1171.2104 1683.398 1035.6425 1818.966
## 2004.2466 1432.286 1174.7241 1689.847 1038.3793 1826.192
## 2004.2493 1436.858 1177.8377 1695.879 1040.7204 1832.996
## 2004.2521 1416.287 1155.8149 1676.759 1017.9294 1814.644
## 2004.2548 1411.420 1149.5048 1673.335 1010.8554 1811.984
## 2004.2575 1425.014 1161.6636 1688.364 1022.2545 1827.773
## 2004.2603 1441.971 1177.1934 1706.748 1037.0287 1846.913
## 2004.2630 1445.312 1179.1152 1711.510 1038.1990 1852.426
## 2004.2658 1440.089 1172.4791 1707.698 1030.8153 1849.362
## 2004.2685 1423.346 1154.3321 1692.360 1011.9246 1834.768
## 2004.2712 1421.460 1151.0481 1691.871 1007.9009 1835.019
## 2004.2740 1429.641 1157.8387 1701.443 1013.9555 1845.326
## 2004.2767 1423.568 1150.3826 1696.753 1005.7671 1841.368
## 2004.2795 1440.073 1165.5112 1714.634 1020.1672 1859.978
## 2004.2822 1444.156 1168.2252 1720.087 1022.1563 1866.156
## 2004.2849 1438.234 1160.9402 1715.527 1014.1499 1862.317
## 2004.2877 1430.042 1151.3926 1708.691 1003.8845 1856.199
## 2004.2904 1432.066 1152.0669 1712.064 1003.8445 1860.287
## 2004.2932 1439.716 1158.3741 1721.057 1009.4408 1869.991
## 2004.2959 1425.906 1143.2279 1708.584 993.5870 1858.225
## 2004.2986 1424.140 1140.1317 1708.149 989.7866 1858.494
## 2004.3014 1430.689 1145.3561 1716.021 994.3102 1867.067
## 2004.3041 1438.680 1152.0299 1725.331 1000.2863 1877.074
## 2004.3068 1442.240 1154.2778 1730.203 1001.8397 1882.641
## 2004.3096 1435.141 1145.8730 1724.410 992.7436 1877.539
## 2004.3123 1438.742 1148.1737 1729.311 994.3561 1883.128
## 2004.3151 1435.071 1143.2087 1726.934 988.7059 1881.437
## 2004.3178 1427.698 1134.5470 1720.850 979.3621 1876.035
## 2004.3205 1432.201 1137.7663 1726.635 981.9022 1882.499
## 2004.3233 1436.334 1140.6225 1732.046 984.0822 1888.586
## 2004.3260 1435.758 1138.7746 1732.742 981.5611 1889.955
## 2004.3288 1440.038 1141.7878 1738.288 983.9038 1896.172
## 2004.3315 1447.775 1148.2636 1747.286 989.7120 1905.837
## 2004.3342 1446.136 1145.3696 1746.903 986.1532 1906.120
## 2004.3370 1434.986 1132.9690 1737.004 973.0906 1896.882
## 2004.3397 1423.746 1120.4834 1727.009 959.9457 1887.547
## 2004.3425 1415.515 1111.0113 1720.018 949.8170 1881.212
## 2004.3452 1437.902 1132.1629 1743.640 970.3147 1905.488
## 2004.3479 1432.427 1125.4584 1739.396 962.9589 1901.896
## 2004.3507 1424.881 1116.6868 1733.075 953.5385 1896.224
## 2004.3534 1426.570 1117.1555 1735.985 953.3611 1899.780
## 2004.3562 1433.804 1123.1738 1744.435 958.7358 1908.873
## 2004.3589 1423.742 1111.8999 1735.583 946.8209 1900.662
## 2004.3616 1419.810 1106.7624 1732.859 941.0447 1898.576
## 2004.3644 1431.566 1117.3165 1745.816 950.9627 1912.170
## 2004.3671 1436.547 1121.0996 1751.993 954.1120 1918.981
## 2004.3699 1432.103 1115.4636 1748.743 947.8447 1916.362
## 2004.3726 1430.575 1112.7469 1748.402 944.4990 1916.650
## 2004.3753 1430.771 1111.7595 1749.782 942.8850 1918.657
## 2004.3781 1433.621 1113.4303 1753.812 943.9315 1923.311
## 2004.3808 1441.633 1120.2675 1762.999 950.1467 1933.120
## 2004.3836 1441.048 1118.5111 1763.584 947.7706 1934.325
## 2004.3863 1435.054 1111.3506 1758.757 939.9926 1930.115
## 2004.3890 1429.231 1104.3658 1754.096 932.3925 1926.070
## 2004.3918 1435.478 1109.4540 1761.501 936.8676 1934.087
## 2004.3945 1434.082 1106.9039 1761.259 933.7066 1934.456
## 2004.3973 1435.865 1107.5373 1764.192 933.7312 1937.999
## 2004.4000 1438.063 1108.5894 1767.537 934.1766 1941.949
## 2004.4027 1437.732 1107.1161 1768.347 932.0987 1943.365
## 2004.4055 1429.961 1098.2078 1761.715 922.5880 1937.335
## 2004.4082 1427.415 1094.5266 1760.302 918.3064 1936.523
## 2004.4110 1439.029 1105.0111 1773.048 928.1925 1949.866
## 2004.4137 1439.716 1104.5711 1774.861 927.1562 1952.276
## 2004.4164 1436.329 1100.0618 1772.597 922.0525 1950.606
## 2004.4192 1443.213 1105.8260 1780.599 927.2243 1959.201
## 2004.4219 1447.946 1109.4441 1786.448 930.2520 1965.640
## 2004.4247 1445.100 1105.4863 1784.713 925.7057 1964.494
## 2004.4274 1443.249 1102.5275 1783.971 922.1604 1964.338
## 2004.4301 1455.480 1113.6535 1797.306 932.7017 1978.257
## 2004.4329 1470.565 1127.6380 1813.492 946.1034 1995.026
## 2004.4356 1474.906 1130.8814 1818.930 948.7659 2001.046
## 2004.4384 1454.883 1109.7652 1800.002 927.0706 1982.696
## 2004.4411 1448.917 1102.7084 1795.126 919.4366 1978.397
## 2004.4438 1448.324 1101.0289 1795.620 917.1817 1979.467
## 2004.4466 1458.181 1109.8023 1806.561 925.3814 1990.982
## 2004.4493 1464.060 1114.6010 1813.520 929.6083 1998.513
## 2004.4521 1467.944 1117.4072 1818.480 931.8444 2004.043
## 2004.4548 1467.931 1116.3214 1819.541 930.1903 2005.673
## 2004.4575 1473.485 1120.8051 1826.166 934.1074 2012.864
## 2004.4603 1474.441 1120.6939 1828.189 933.4313 2015.451
## 2004.4630 1471.143 1116.3318 1825.955 928.5060 2013.780
## 2004.4658 1467.304 1111.4318 1823.176 923.0445 2011.563
## 2004.4685 1466.007 1109.0776 1822.937 920.1304 2011.884
## 2004.4712 1466.048 1108.0635 1824.032 918.5582 2013.537
## 2004.4740 1463.287 1104.2514 1822.322 914.1895 2012.384
## 2004.4767 1464.459 1104.3749 1824.542 913.7581 2015.159
## 2004.4795 1473.047 1111.9182 1834.176 920.7480 2025.346
## 2004.4822 1483.708 1121.5366 1845.879 929.8147 2037.601
## 2004.4849 1479.374 1116.1636 1842.585 923.8917 2034.857
## 2004.4877 1471.886 1107.6391 1836.132 914.8185 2028.953
## 2004.4904 1463.629 1098.3485 1828.909 904.9809 2022.276
## 2004.4932 1461.637 1095.3264 1827.947 901.4134 2021.860
## 2004.4959 1463.478 1096.1405 1830.816 901.6836 2025.273
## 2004.4986 1467.187 1098.8243 1835.550 903.8249 2030.549
## 2004.5014 1463.442 1094.0578 1832.827 898.5175 2028.367
## 2004.5041 1466.036 1095.6323 1836.439 899.5526 2032.519
## 2004.5068 1471.486 1100.0662 1842.905 903.4485 2039.523
## 2004.5096 1482.652 1110.2194 1855.086 913.0653 2052.240
## 2004.5123 1478.892 1105.4487 1852.336 907.7595 2050.025
## 2004.5151 1467.885 1093.4338 1842.337 895.2110 2040.560
## 2004.5178 1464.070 1088.6130 1839.527 889.8581 2038.282
## 2004.5205 1466.013 1089.5533 1842.472 890.2677 2041.758
## 2004.5233 1468.248 1090.7883 1845.707 890.9734 2045.522
## 2004.5260 1456.786 1078.3293 1835.242 877.9865 2035.585
## 2004.5288 1449.451 1069.9996 1828.902 869.1302 2029.771
## 2004.5315 1456.095 1075.6521 1836.539 874.2576 2037.933
## 2004.5342 1463.612 1082.1797 1845.045 880.2614 2046.963
## 2004.5370 1474.209 1091.7893 1856.628 889.3486 2059.069
## 2004.5397 1468.815 1085.4115 1852.219 882.4498 2055.181
## 2004.5425 1457.312 1072.9260 1841.698 869.4445 2045.179
## 2004.5452 1455.411 1070.0459 1840.776 866.0459 2044.776
## 2004.5479 1463.888 1077.5457 1850.230 873.0286 2054.747
## 2004.5507 1472.913 1085.5971 1860.230 880.5642 2065.263
## 2004.5534 1461.546 1073.2575 1849.834 867.7101 2055.381
## 2004.5562 1454.605 1065.3477 1843.863 859.2871 2049.924
## 2004.5589 1463.420 1073.1954 1853.645 866.6229 2060.218
## 2004.5616 1471.629 1080.4397 1862.819 873.3565 2069.902
## 2004.5644 1472.404 1080.2524 1864.556 872.6597 2072.149
## 2004.5671 1471.025 1077.9127 1864.136 869.8118 2072.237
## 2004.5699 1474.854 1080.7844 1868.924 872.1766 2077.531
## 2004.5726 1476.485 1081.4597 1871.509 872.3462 2080.623
## 2004.5753 1476.008 1080.0303 1871.986 870.4122 2081.604
## 2004.5781 1475.905 1078.9760 1872.833 868.8547 2082.955
## 2004.5808 1469.166 1071.2894 1867.044 860.6660 2077.667
## 2004.5836 1460.005 1061.1815 1858.828 850.0572 2069.952
## 2004.5863 1467.291 1067.5238 1867.058 855.8998 2078.682
## 2004.5890 1477.914 1077.2050 1878.623 865.0825 2090.745
## 2004.5918 1482.154 1080.5051 1883.802 867.8853 2096.422
## 2004.5945 1475.471 1072.8851 1878.057 859.7690 2091.173
## 2004.5973 1467.428 1063.9070 1870.949 850.2959 2084.560
## 2004.6000 1464.719 1060.2652 1869.173 846.1602 2083.278
## 2004.6027 1464.468 1059.0831 1869.853 844.4854 2084.451
## 2004.6055 1459.530 1053.2162 1865.843 838.1268 2080.933
## 2004.6082 1458.316 1051.0760 1865.556 835.4961 2081.136
## 2004.6110 1463.672 1055.5078 1871.837 839.4385 2087.906
## 2004.6137 1467.345 1058.2579 1876.432 841.7003 2092.990
## 2004.6164 1459.591 1049.5836 1869.598 832.5388 2086.643
## 2004.6192 1449.698 1038.7720 1860.623 821.2411 2078.154
## 2004.6219 1449.224 1037.3819 1861.066 819.3660 2079.082
## 2004.6247 1450.418 1037.6621 1863.174 819.1622 2081.674
## 2004.6274 1443.814 1030.1457 1857.482 811.1630 2076.465
## 2004.6301 1434.443 1019.8643 1849.021 800.3998 2068.486
## 2004.6329 1439.837 1024.3505 1855.324 804.4052 2075.269
## 2004.6356 1442.668 1026.2752 1859.061 805.8502 2079.486
## 2004.6384 1432.493 1015.1964 1849.790 794.2928 2070.694
## 2004.6411 1431.912 1013.7123 1850.111 792.3310 2071.492
## 2004.6438 1450.044 1030.9442 1869.143 809.0863 2091.001
## 2004.6466 1456.178 1036.1802 1876.176 813.8467 2098.510
## 2004.6493 1439.292 1018.3976 1860.186 795.5896 2082.995
## 2004.6521 1433.595 1011.8062 1855.384 788.5246 2078.666
## 2004.6548 1432.217 1009.5355 1854.899 785.7813 2078.653
## 2004.6575 1444.715 1021.1425 1868.287 796.9168 2092.513
## 2004.6603 1447.506 1023.0450 1871.968 798.3487 2096.664
## 2004.6630 1439.861 1014.5122 1865.209 789.3464 2090.375
## 2004.6658 1431.608 1005.3748 1857.842 779.7403 2083.477
## 2004.6685 1441.071 1013.9540 1868.188 787.8519 2094.290
## 2004.6712 1437.083 1009.0845 1865.082 782.5157 2091.651
## 2004.6740 1432.676 1003.7975 1861.554 776.7630 2088.589
## 2004.6767 1433.040 1003.2834 1862.796 775.7841 2090.295
## 2004.6795 1421.810 991.1771 1852.442 763.2140 2080.405
## 2004.6822 1404.419 972.9124 1835.926 744.4864 2064.352
## 2004.6849 1418.693 986.3131 1851.072 757.4252 2079.960
## 2004.6877 1441.328 1008.0779 1874.579 778.7291 2103.927
## 2004.6904 1444.448 1010.3287 1878.568 780.5198 2108.377
## 2004.6932 1441.629 1006.6427 1876.616 776.3746 2106.884
## 2004.6959 1436.454 1000.6017 1872.307 769.8754 2103.033
## 2004.6986 1431.186 994.4699 1867.903 763.2863 2099.086
## 2004.7014 1420.425 982.8461 1858.003 751.2059 2089.643
## 2004.7041 1423.184 984.7446 1861.623 752.6489 2093.718
## 2004.7068 1443.375 1004.0765 1882.672 771.5262 2115.223
## 2004.7096 1444.643 1004.4880 1884.798 771.4840 2117.802
## 2004.7123 1442.310 1001.2991 1883.320 767.8422 2116.777
## 2004.7151 1429.821 987.9563 1871.685 754.0474 2105.594
## 2004.7178 1430.133 987.4165 1872.850 753.0565 2107.210
## 2004.7205 1444.855 1001.2878 1888.422 766.4775 2123.233
## 2004.7233 1450.046 1005.6298 1894.462 770.3701 2129.722
## 2004.7260 1441.737 996.4731 1887.000 760.7649 2122.708
## 2004.7288 1429.017 982.9081 1875.126 746.7521 2111.282
## 2004.7315 1435.649 988.6955 1882.602 752.0927 2119.205
## 2004.7342 1447.085 999.2892 1894.881 762.2404 2131.930
## 2004.7370 1458.632 1009.9952 1907.269 772.5013 2144.763
## 2004.7397 1454.089 1004.6132 1903.565 766.6749 2141.504
## 2004.7425 1456.052 1005.7383 1906.366 767.3565 2144.748
## 2004.7452 1453.218 1002.0679 1904.368 763.2434 2143.193
## 2004.7479 1438.838 986.8531 1890.823 747.5868 2130.089
## 2004.7507 1431.405 978.5875 1884.223 738.8801 2123.931
## 2004.7534 1445.385 991.7356 1899.035 751.5880 2139.182
## 2004.7562 1447.742 993.2627 1902.222 752.6757 2142.809
## 2004.7589 1449.299 993.9903 1904.607 752.9646 2145.632
## 2004.7616 1442.973 986.8375 1899.108 745.3740 2140.572
## 2004.7644 1425.057 968.0956 1882.018 726.1951 2123.918
## 2004.7671 1425.155 967.3695 1882.940 725.0327 2125.276
## 2004.7699 1431.387 972.7793 1889.995 730.0071 2132.767
## 2004.7726 1448.337 988.9081 1907.766 745.7012 2150.973
## 2004.7753 1459.133 998.8848 1919.382 755.2439 2163.023
## 2004.7781 1459.754 998.6871 1920.821 754.6131 2164.894
## 2004.7808 1457.696 995.8129 1919.580 751.3065 2164.086
## 2004.7836 1457.920 995.2211 1920.619 750.2831 2165.557
## 2004.7863 1450.966 987.4532 1914.479 742.0844 2159.847
## 2004.7890 1465.022 1000.6972 1929.348 754.8983 2175.146
## 2004.7918 1479.180 1014.0439 1944.316 767.8157 2190.545
## 2004.7945 1479.152 1013.2061 1945.098 766.5492 2191.755
## 2004.7973 1476.709 1009.9554 1943.464 762.8707 2190.548
## 2004.8000 1465.652 998.0913 1933.213 750.5795 2180.725
## 2004.8027 1458.371 990.0050 1926.738 742.0668 2174.676
## 2004.8055 1470.220 1001.0497 1939.390 752.6858 2187.754
## 2004.8082 1471.542 1001.5694 1941.516 752.7807 2190.304
## 2004.8110 1465.537 994.7629 1936.312 745.5500 2185.525
## 2004.8137 1433.762 962.1878 1905.337 712.5514 2154.973
## 2004.8164 1434.567 962.1940 1906.940 712.1349 2156.999
## 2004.8192 1440.625 967.4543 1913.795 716.9731 2164.276
## 2004.8219 1423.006 949.0400 1896.972 698.1375 2147.875
## 2004.8247 1450.604 975.8435 1925.365 724.5204 2176.688
## 2004.8274 1445.589 970.0350 1921.143 718.2919 2172.886
## 2004.8301 1440.754 964.4083 1917.100 712.2460 2169.262
## 2004.8329 1431.504 954.3675 1908.641 701.7867 2161.221
## 2004.8356 1439.339 961.4132 1917.265 708.4145 2170.263
## 2004.8384 1441.028 962.3142 1919.742 708.8984 2173.158
## 2004.8411 1427.367 947.8664 1906.868 694.0342 2160.700
## 2004.8438 1437.166 956.8801 1917.452 702.6321 2171.700
## 2004.8466 1449.232 968.1622 1930.302 713.4990 2184.966
## 2004.8493 1456.815 974.9622 1938.668 719.8846 2193.746
## 2004.8521 1464.004 981.3698 1946.639 725.8785 2202.130
## 2004.8548 1448.065 964.6505 1931.480 708.7461 2187.385
## 2004.8575 1450.877 966.6831 1935.071 710.3663 2191.388
## 2004.8603 1426.889 941.9170 1911.861 685.1884 2168.589
## 2004.8630 1408.953 923.2046 1894.701 666.0649 2151.841
## 2004.8658 1407.753 921.2294 1894.277 663.6793 2151.827
## 2004.8685 1413.682 926.3840 1900.980 668.4241 2158.939
## 2004.8712 1427.769 939.6982 1915.840 681.3292 2174.209
## 2004.8740 1434.426 945.5838 1923.268 686.8063 2182.046
## 2004.8767 1431.729 942.1166 1921.342 682.9312 2180.527
## 2004.8795 1430.955 940.5730 1921.337 680.9805 2180.930
## 2004.8822 1438.667 947.5173 1929.817 687.5182 2189.817
## 2004.8849 1438.769 946.8522 1930.686 686.4471 2191.091
## 2004.8877 1432.008 939.3256 1924.691 678.5153 2185.501
## 2004.8904 1424.278 930.8308 1917.725 669.6158 2178.940
## 2004.8932 1440.524 946.3137 1934.734 684.6946 2196.353
## 2004.8959 1439.810 944.8382 1934.783 682.8157 2196.805
## 2004.8986 1435.734 940.0012 1931.468 677.5759 2193.893
## 2004.9014 1431.617 935.1245 1928.110 672.2970 2190.938
## 2004.9041 1435.508 938.2563 1932.759 675.0272 2195.988
## 2004.9068 1425.497 927.4879 1923.506 663.8579 2187.136
## 2004.9096 1428.884 930.1191 1927.649 666.0887 2191.680
## 2004.9123 1429.754 930.2338 1929.275 665.8038 2193.705
## 2004.9151 1409.446 909.1715 1909.720 644.3422 2174.549
## 2004.9178 1410.066 909.0385 1911.093 643.8107 2176.321
## 2004.9205 1416.981 915.2024 1918.760 649.5767 2184.386
## 2004.9233 1424.422 921.8923 1926.951 655.8692 2192.974
## 2004.9260 1436.617 933.3382 1939.896 666.9184 2206.316
## 2004.9288 1431.448 927.4209 1935.476 660.6049 2202.292
## 2004.9315 1422.210 917.4350 1926.984 650.2234 2194.196
## 2004.9342 1439.264 933.7435 1944.785 666.1370 2212.392
## 2004.9370 1439.193 932.9276 1945.459 664.9267 2213.460
## 2004.9397 1435.640 928.6304 1942.650 660.2356 2211.045
## 2004.9425 1429.844 922.0915 1937.597 653.3035 2206.385
## 2004.9452 1441.651 933.1566 1950.146 663.9759 2219.326
## 2004.9479 1433.576 924.3411 1942.811 654.7683 2212.384
## 2004.9507 1434.063 924.0883 1944.038 654.1239 2214.002
## 2004.9534 1439.288 928.5748 1950.001 658.2194 2220.357
## 2004.9562 1425.715 914.2641 1937.166 643.5184 2207.912
## 2004.9589 1435.498 923.3111 1947.686 652.1755 2218.821
## 2004.9616 1437.877 924.9548 1950.800 653.4299 2222.325
## 2004.9644 1428.158 914.5009 1941.815 642.5874 2213.728
## 2004.9671 1424.275 909.8846 1938.665 637.5829 2210.967
## 2004.9699 1440.429 925.3070 1955.552 652.6176 2228.241
## 2004.9726 1448.327 932.4730 1964.180 659.3966 2237.257
## 2004.9753 1445.385 928.8009 1961.969 655.3380 2235.432
## 2004.9781 1441.604 924.2909 1958.917 650.4420 2232.766
## 2004.9808 1423.688 905.6473 1941.729 631.4129 2215.964
## 2004.9836 1414.803 896.0349 1933.571 621.4157 2208.190
## 2004.9863 1410.359 890.8650 1929.853 615.8614 2204.857
## 2004.9890 1409.275 889.0556 1929.494 613.6682 2204.881
## 2004.9918 1423.595 902.6521 1944.539 626.8814 2220.309
## 2004.9945 1430.756 909.0897 1952.422 632.9363 2228.576
## 2004.9973 1446.112 923.7239 1968.501 647.1882 2245.036
## 2005.0000 1443.563 920.4535 1966.672 643.5361 2243.590
## 2005.0027 1445.544 921.7143 1969.373 644.4158 2246.672
## 2005.0055 1445.009 920.4606 1969.557 642.7814 2247.237
## 2005.0082 1455.408 930.1410 1980.674 652.0817 2258.733
## 2005.0110 1450.174 924.1907 1976.158 645.7518 2254.597
## 2005.0137 1449.436 922.7361 1976.135 643.9181 2254.953
## 2005.0164 1420.343 892.9286 1947.758 613.7321 2226.955
## 2005.0192 1405.574 877.4446 1933.703 597.8700 2213.277
## 2005.0219 1424.431 895.5889 1953.273 615.6367 2233.226
## 2005.0247 1436.933 907.3783 1966.487 627.0491 2246.816
## 2005.0274 1430.573 900.3072 1960.839 619.6014 2241.544
## 2005.0301 1420.404 889.4279 1951.380 608.3462 2232.462
## 2005.0329 1421.944 890.2585 1953.629 608.8013 2235.087
## 2005.0356 1433.895 901.5016 1966.289 619.6693 2248.122
## 2005.0384 1433.117 900.0155 1966.218 617.8087 2248.425
## 2005.0411 1417.577 883.7689 1951.385 601.1880 2233.966
## 2005.0438 1406.612 872.0984 1941.126 589.1440 2224.080
## 2005.0466 1404.724 869.5061 1939.943 586.1787 2223.270
## 2005.0493 1415.348 879.4258 1951.270 595.7258 2234.970
## 2005.0521 1434.186 897.5615 1970.811 613.4894 2254.883
## 2005.0548 1455.310 917.9836 1992.637 633.5400 2277.081
## 2005.0575 1444.418 906.3906 1982.446 621.5758 2267.261
## 2005.0603 1450.817 912.0887 1989.545 626.9034 2274.730
## 2005.0630 1445.513 906.0863 1984.941 620.5308 2270.496
## 2005.0658 1419.866 879.7402 1959.991 593.8151 2245.916
## 2005.0685 1412.971 872.1485 1953.794 585.8542 2240.089
## 2005.0712 1427.331 885.8116 1968.850 599.1486 2255.513
## 2005.0740 1429.448 887.2330 1971.663 600.2018 2258.694
## 2005.0767 1424.141 881.2313 1967.051 593.8323 2254.450
## 2005.0795 1439.794 896.1902 1983.397 608.4239 2271.163
## 2005.0822 1428.464 884.1681 1972.761 596.0350 2260.894
## 2005.0849 1397.517 852.5287 1942.505 564.0292 2231.005
## 2005.0877 1416.996 871.3166 1962.676 582.4513 2251.541
## 2005.0904 1424.781 878.4112 1971.151 589.1804 2260.382
## 2005.0932 1427.872 880.8124 1974.931 591.2167 2264.527
## 2005.0959 1429.397 881.6489 1977.145 591.6887 2267.105
## 2005.0986 1428.660 880.2247 1977.096 589.9005 2267.420
## 2005.1014 1435.094 885.9718 1984.217 595.2840 2274.904
## 2005.1041 1438.982 889.1737 1988.790 598.1227 2279.841
## 2005.1068 1443.297 892.8038 1993.791 601.3901 2285.204
## 2005.1096 1433.449 882.2710 1984.626 590.4951 2276.402
## 2005.1123 1414.543 862.6815 1966.404 570.5438 2258.541
## 2005.1151 1403.567 851.0228 1956.110 558.5239 2248.609
## 2005.1178 1405.912 852.6863 1959.137 559.8264 2251.997
## 2005.1205 1420.234 866.3281 1974.141 573.1078 2267.361
## 2005.1233 1432.160 877.5736 1986.746 583.9933 2280.327
## 2005.1260 1418.327 863.0614 1973.593 569.1216 2267.533
## 2005.1288 1413.408 857.4638 1969.352 563.1648 2263.651
## 2005.1315 1401.204 844.5824 1957.826 549.9247 2252.483
## 2005.1342 1393.419 836.1202 1950.717 541.1043 2245.733
## 2005.1370 1405.684 847.7100 1963.659 552.3363 2259.032
## 2005.1397 1434.896 876.2470 1993.546 580.5159 2289.277
## 2005.1425 1430.689 871.3652 1990.013 575.2771 2286.101
## 2005.1452 1422.273 862.2763 1982.271 565.8317 2278.715
## 2005.1479 1411.613 850.9428 1972.282 554.1421 2269.083
## 2005.1507 1393.133 831.7916 1954.475 534.6353 2251.631
## 2005.1534 1393.228 831.2157 1955.241 533.7041 2252.753
## 2005.1562 1394.356 831.6726 1957.039 533.8063 2254.905
## 2005.1589 1386.343 822.9903 1949.695 524.7695 2247.916
## 2005.1616 1403.492 839.4708 1967.513 540.8961 2266.088
## 2005.1644 1417.810 853.1206 1982.499 554.1923 2281.427
## 2005.1671 1385.675 820.3184 1951.031 521.0370 2250.312
## 2005.1699 1394.340 828.3174 1960.362 528.6832 2259.996
## 2005.1726 1413.050 846.3625 1979.738 546.3760 2279.725
## 2005.1753 1411.571 844.2184 1978.924 543.8801 2279.262
## 2005.1781 1389.549 821.5321 1957.565 520.8423 2258.255
## 2005.1808 1377.954 809.2744 1946.634 508.2335 2247.675
## 2005.1836 1392.794 823.4520 1962.136 522.0605 2263.528
## 2005.1863 1446.625 876.6216 2016.629 574.8798 2318.371
## 2005.1890 1456.179 885.5139 2026.843 583.4222 2328.935
## 2005.1918 1437.790 866.4649 2009.115 564.0238 2311.556
## 2005.1945 1433.818 861.8339 2005.802 559.0438 2308.592
## 2005.1973 1435.703 863.0605 2008.346 559.9217 2311.485
## 2005.2000 1428.783 855.4828 2002.084 551.9958 2305.571
## 2005.2027 1407.770 833.8125 1981.728 529.9777 2285.563
## 2005.2055 1381.732 807.1176 1956.346 502.9353 2260.528
## 2005.2082 1387.471 812.2017 1962.741 507.6724 2267.270
## 2005.2110 1396.179 820.2545 1972.103 515.3786 2276.979
## 2005.2137 1411.198 834.6196 1987.777 529.3974 2292.999
## 2005.2164 1403.995 826.7634 1981.227 521.1954 2286.795
## 2005.2192 1410.955 833.0710 1988.840 527.1575 2294.753
## 2005.2219 1438.958 860.4218 2017.494 554.1632 2323.753
## 2005.2247 1456.357 877.1696 2035.544 570.5663 2342.148
## 2005.2274 1456.336 876.4979 2036.174 569.5503 2343.121
## 2005.2301 1440.118 859.6306 2020.606 552.3391 2327.897
## 2005.2329 1416.225 835.0889 1997.362 527.4539 2304.997
## 2005.2356 1429.560 847.7756 2011.345 539.7973 2319.323
## 2005.2384 1436.662 854.2302 2019.095 545.9092 2327.416
## 2005.2411 1422.209 839.1301 2005.288 530.4667 2313.952
## 2005.2438 1427.304 843.5792 2011.029 534.5738 2320.035
## 2005.2466 1432.286 847.9152 2016.656 538.5681 2326.003
## 2005.2493 1436.858 851.8434 2021.874 542.1551 2331.562
## 2005.2521 1416.287 830.6277 2001.946 520.5986 2311.975
## 2005.2548 1411.420 825.1174 1997.722 514.7478 2308.092
## 2005.2575 1425.014 838.0688 2011.958 527.3591 2322.668
## 2005.2603 1441.971 854.3843 2029.557 543.3347 2340.607
## 2005.2630 1445.312 857.0847 2033.540 545.6957 2344.929
## 2005.2658 1440.089 851.2204 2028.957 539.4924 2340.685
## 2005.2685 1423.346 833.8384 2012.854 521.7718 2324.921
## 2005.2712 1421.460 831.3129 2011.607 518.9080 2324.012
## 2005.2740 1429.641 838.8554 2020.426 526.1126 2333.169
## 2005.2767 1423.568 832.1448 2014.991 519.0645 2328.071
## 2005.2795 1440.073 848.0128 2032.132 534.5952 2345.550
## 2005.2822 1444.156 851.4598 2036.852 537.7055 2350.607
## 2005.2849 1438.234 844.9019 2031.565 530.8110 2345.656
## 2005.2877 1430.042 836.0753 2024.009 521.6484 2338.436
## 2005.2904 1432.066 837.4647 2026.667 522.7020 2341.429
## 2005.2932 1439.716 844.4813 2034.950 529.3832 2350.048
## 2005.2959 1425.906 830.0388 2021.773 514.6056 2337.207
## 2005.2986 1424.140 827.6406 2020.640 511.8728 2336.408
## 2005.3014 1430.689 833.5576 2027.820 517.4554 2343.922
## 2005.3041 1438.680 840.9184 2036.442 524.4823 2352.878
## 2005.3068 1442.240 843.8479 2040.632 527.0782 2357.402
## 2005.3096 1435.141 836.1195 2034.163 519.0166 2351.266
## 2005.3123 1438.742 839.0915 2038.393 521.6556 2355.829
## 2005.3151 1435.071 834.7925 2035.350 517.0240 2353.119
## 2005.3178 1427.698 826.7918 2028.605 508.6911 2346.705
## 2005.3205 1432.201 830.6672 2033.734 512.2346 2352.167
## 2005.3233 1436.334 834.1744 2038.494 515.4104 2357.258
## 2005.3260 1435.758 832.9729 2038.543 513.8776 2357.639
## 2005.3288 1440.038 836.6275 2043.448 517.2014 2362.874
## 2005.3315 1447.775 843.7401 2051.809 523.9835 2371.566
## 2005.3342 1446.136 841.4782 2050.795 521.3914 2370.881
## 2005.3370 1434.986 829.7051 2040.268 509.2886 2360.684
## 2005.3397 1423.746 817.8426 2029.650 497.0965 2350.396
## 2005.3425 1415.515 808.9891 2022.040 487.9139 2343.115
## 2005.3452 1437.902 830.7549 2045.048 509.3509 2366.452
## 2005.3479 1432.427 824.6602 2040.194 502.9278 2361.927
## 2005.3507 1424.881 816.4942 2033.268 494.4336 2355.329
## 2005.3534 1426.570 817.5642 2035.577 495.1759 2357.965
## 2005.3562 1433.804 824.1797 2043.429 501.4639 2366.145
## 2005.3589 1423.742 813.4989 2033.984 490.4560 2357.027
## 2005.3616 1419.810 808.9504 2030.671 485.5806 2354.040
## 2005.3644 1431.566 820.0896 2043.043 496.3933 2366.739
## 2005.3671 1436.547 824.4536 2048.639 500.4312 2372.662
## 2005.3699 1432.103 819.3948 2044.812 495.0466 2369.160
## 2005.3726 1430.575 817.2514 2043.898 492.5777 2368.572
## 2005.3753 1430.771 816.8335 2044.708 491.8346 2369.707
## 2005.3781 1433.621 819.0700 2048.172 493.7463 2373.496
## 2005.3808 1441.633 826.4692 2056.797 500.8210 2382.446
## 2005.3836 1441.048 825.2711 2056.824 499.2987 2382.797
## 2005.3863 1435.054 818.6653 2051.442 492.3691 2377.738
## 2005.3890 1429.231 812.2316 2046.231 485.6118 2372.850
## 2005.3918 1435.478 817.8674 2053.088 490.9244 2380.031
## 2005.3945 1434.082 815.8614 2052.302 488.5955 2379.568
## 2005.3973 1435.865 817.0354 2054.694 489.4469 2382.283
## 2005.4000 1438.063 818.6247 2057.501 490.7139 2385.412
## 2005.4027 1437.732 817.6852 2057.778 489.4525 2386.011
## 2005.4055 1429.961 809.3075 2050.616 480.7531 2379.170
## 2005.4082 1427.415 806.1535 2048.676 477.2778 2377.551
## 2005.4110 1439.029 817.1619 2060.897 487.9652 2390.094
## 2005.4137 1439.716 817.2426 2062.189 487.7252 2391.707
## 2005.4164 1436.329 813.2509 2059.408 483.4131 2389.246
## 2005.4192 1443.213 819.5294 2066.896 489.3715 2397.054
## 2005.4219 1447.946 823.6588 2072.233 493.1812 2402.711
## 2005.4247 1445.100 820.2092 2069.990 489.4121 2400.788
## 2005.4274 1443.249 817.7556 2068.743 486.6393 2399.859
## 2005.4301 1455.480 829.3837 2081.575 497.9486 2413.010
## 2005.4329 1470.565 843.8674 2097.263 512.1138 2429.016
## 2005.4356 1474.906 847.6070 2102.204 515.5352 2434.276
## 2005.4384 1454.883 826.9841 2082.783 494.5943 2415.172
## 2005.4411 1448.917 820.4177 2077.416 487.7103 2410.124
## 2005.4438 1448.324 819.2258 2077.423 486.2011 2410.448
## 2005.4466 1458.181 828.4839 2087.879 495.1422 2421.221
## 2005.4493 1464.060 833.7646 2094.356 500.1061 2428.015
## 2005.4521 1467.944 837.0500 2098.837 503.0751 2432.812
## 2005.4548 1467.931 836.4407 2099.422 502.1498 2433.713
## 2005.4575 1473.485 841.3982 2105.573 506.7914 2440.180
## 2005.4603 1474.441 841.7581 2107.125 506.8358 2442.047
## 2005.4630 1471.143 837.8644 2104.422 502.6268 2439.660
## 2005.4658 1467.304 833.4303 2101.178 497.8778 2436.730
## 2005.4685 1466.007 831.5392 2100.475 495.6721 2436.342
## 2005.4712 1466.048 830.9858 2101.110 494.8044 2437.291
## 2005.4740 1463.287 827.6318 2098.942 491.1364 2435.437
## 2005.4767 1464.459 828.2109 2100.706 491.4017 2437.516
## 2005.4795 1473.047 836.2073 2109.887 499.0846 2447.010
## 2005.4822 1483.708 846.2763 2121.139 508.8404 2458.575
## 2005.4849 1479.374 841.3516 2117.397 503.6028 2455.145
## 2005.4877 1471.886 833.2728 2110.499 495.2115 2448.560
## 2005.4904 1463.629 824.4256 2102.831 486.0520 2441.205
## 2005.4932 1461.637 821.8445 2101.429 483.1589 2440.115
## 2005.4959 1463.478 823.0973 2103.860 484.0999 2442.857
## 2005.4986 1467.187 826.2174 2108.156 486.9087 2447.465
## 2005.5014 1463.442 821.8849 2104.999 482.2650 2444.619
## 2005.5041 1466.036 823.8912 2108.180 483.9604 2448.111
## 2005.5068 1471.486 828.7545 2114.217 488.5132 2454.458
## 2005.5096 1482.652 839.3351 2125.970 498.7834 2466.522
## 2005.5123 1478.892 834.9894 2122.795 494.1277 2463.657
## 2005.5151 1467.885 823.3973 2112.374 482.2259 2453.545
## 2005.5178 1464.070 818.9972 2109.143 477.5164 2450.623
## 2005.5205 1466.013 820.3560 2111.669 478.5660 2453.460
## 2005.5233 1468.248 822.0074 2114.488 479.9085 2456.587
## 2005.5260 1456.786 809.9626 2103.609 467.5551 2446.017
## 2005.5288 1449.451 802.0451 2096.857 459.3292 2439.572
## 2005.5315 1456.095 808.1077 2104.083 465.0838 2447.107
## 2005.5342 1463.612 815.0433 2112.181 471.7116 2455.513
## 2005.5370 1474.209 825.0589 2123.359 481.4197 2466.998
## 2005.5397 1468.815 819.0852 2118.546 475.1387 2462.492
## 2005.5425 1457.312 807.0016 2107.622 462.7482 2451.875
## 2005.5452 1455.411 804.5215 2106.301 459.9614 2450.861
## 2005.5479 1463.888 812.4193 2115.356 467.5528 2460.222
## 2005.5507 1472.913 820.8668 2124.960 475.6941 2470.133
## 2005.5534 1461.546 808.9213 2114.170 463.4428 2459.649
## 2005.5562 1454.605 801.4037 2107.807 455.6196 2453.591
## 2005.5589 1463.420 809.6418 2117.199 463.5523 2463.288
## 2005.5616 1471.629 817.2745 2125.984 470.8800 2472.379
## 2005.5644 1472.404 817.4737 2127.335 470.7744 2474.034
## 2005.5671 1471.025 815.5188 2126.530 468.5150 2473.534
## 2005.5699 1474.854 818.7734 2130.935 471.4653 2478.243
## 2005.5726 1476.485 819.8298 2133.139 472.2177 2480.751
## 2005.5753 1476.008 818.7796 2133.237 470.8638 2481.152
## 2005.5781 1475.905 818.1028 2133.706 469.8836 2481.926
## 2005.5808 1469.166 810.7919 2127.541 462.2695 2476.063
## 2005.5836 1460.005 801.0580 2118.952 452.2326 2467.777
## 2005.5863 1467.291 807.7725 2126.810 458.6444 2475.938
## 2005.5890 1477.914 817.8242 2138.004 468.3937 2487.434
## 2005.5918 1482.154 821.4930 2142.814 471.7604 2492.547
## 2005.5945 1475.471 814.2400 2136.702 464.2056 2486.736
## 2005.5973 1467.428 805.6274 2129.229 455.2913 2479.565
## 2005.6000 1464.719 802.3493 2127.089 451.7118 2477.727
## 2005.6027 1464.468 801.5292 2127.407 450.5907 2478.345
## 2005.6055 1459.530 796.0227 2123.037 444.7833 2474.276
## 2005.6082 1458.316 794.2413 2122.391 442.7013 2473.931
## 2005.6110 1463.672 799.0302 2128.315 447.1899 2480.155
## 2005.6137 1467.345 802.1358 2132.554 449.9954 2484.694
## 2005.6164 1459.591 793.8155 2125.366 441.3753 2477.807
## 2005.6192 1449.698 783.3563 2116.039 430.6165 2468.779
## 2005.6219 1449.224 782.3170 2116.131 429.2779 2469.170
## 2005.6247 1450.418 782.9464 2117.890 429.6082 2471.228
## 2005.6274 1443.814 775.7778 2111.850 422.1408 2465.487
## 2005.6301 1434.443 765.8426 2103.043 411.9070 2456.978
## 2005.6329 1439.837 770.6734 2109.001 416.4396 2463.235
## 2005.6356 1442.668 772.9413 2112.395 418.4094 2466.927
## 2005.6384 1432.493 762.2042 2102.783 407.3745 2457.612
## 2005.6411 1431.912 761.0602 2102.763 405.9330 2457.890
## 2005.6438 1450.044 778.6308 2121.457 423.2062 2476.881
## 2005.6466 1456.178 784.2041 2128.152 428.4825 2483.874
## 2005.6493 1439.292 766.7573 2111.827 410.7389 2467.845
## 2005.6521 1433.595 760.5002 2106.690 404.1852 2463.005
## 2005.6548 1432.217 758.5624 2105.872 401.9511 2462.483
## 2005.6575 1444.715 770.5009 2118.929 413.5936 2475.836
## 2005.6603 1447.506 772.7336 2122.279 415.5304 2479.482
## 2005.6630 1439.861 764.5295 2115.192 407.0307 2472.691
## 2005.6658 1431.608 755.7193 2107.498 397.9253 2465.292
## 2005.6685 1441.071 764.6245 2117.518 406.5354 2475.607
## 2005.6712 1437.083 760.0796 2114.087 401.6956 2472.471
## 2005.6740 1432.676 755.1159 2110.236 396.4373 2468.914
## 2005.6767 1433.040 754.9236 2111.156 395.9506 2470.129
## 2005.6795 1421.810 743.1379 2100.481 383.8708 2459.748
## 2005.6822 1404.419 725.1924 2083.646 365.6315 2443.207
## 2005.6849 1418.693 738.9110 2098.474 379.0564 2458.329
## 2005.6877 1441.328 760.9925 2121.664 400.8445 2481.812
## 2005.6904 1444.448 763.5586 2125.338 403.1174 2485.779
## 2005.6932 1441.629 760.1866 2123.072 399.4525 2483.806
## 2005.6959 1436.454 754.4583 2118.450 393.4316 2479.477
## 2005.6986 1431.186 748.6381 2113.735 387.3189 2475.054
## 2005.7014 1420.425 737.3244 2103.525 375.7130 2465.136
## 2005.7041 1423.184 739.5319 2106.836 377.6285 2468.739
## 2005.7068 1443.375 759.1716 2127.577 396.9765 2489.773
## 2005.7096 1444.643 759.8896 2129.397 397.4030 2491.883
## 2005.7123 1442.310 757.0059 2127.614 394.2280 2490.391
## 2005.7151 1429.821 743.9672 2115.674 380.8982 2478.743
## 2005.7178 1430.133 743.7303 2116.536 380.3705 2479.896
## 2005.7205 1444.855 757.9032 2131.807 394.2529 2495.457
## 2005.7233 1450.046 762.5457 2137.546 398.6050 2501.487
## 2005.7260 1441.737 753.6883 2129.785 389.4575 2494.016
## 2005.7288 1429.017 740.4213 2117.613 375.9007 2482.134
## 2005.7315 1435.649 746.5058 2124.792 381.6955 2489.602
## 2005.7342 1447.085 757.3952 2136.775 392.2955 2501.875
## 2005.7370 1458.632 768.3959 2148.868 403.0070 2514.257
## 2005.7397 1454.089 763.3074 2144.871 397.6295 2510.549
## 2005.7425 1456.052 764.7248 2147.380 398.7582 2513.346
## 2005.7452 1453.218 761.3457 2145.090 395.0906 2511.345
## 2005.7479 1438.838 746.4210 2131.255 379.8777 2497.798
## 2005.7507 1431.405 738.4444 2124.366 371.6129 2491.198
## 2005.7534 1445.385 751.8804 2138.890 384.7611 2506.009
## 2005.7562 1447.742 753.6944 2141.790 386.2875 2509.197
## 2005.7589 1449.299 754.7076 2143.889 387.0134 2511.584
## 2005.7616 1442.973 747.8395 2138.106 379.8581 2506.088
## 2005.7644 1425.057 729.3812 2120.732 361.1129 2489.000
## 2005.7671 1425.155 728.9375 2121.371 360.3825 2489.926
## 2005.7699 1431.387 734.6288 2128.145 365.7874 2496.987
## 2005.7726 1448.337 751.0380 2145.636 381.9103 2514.764
## 2005.7753 1459.133 761.2940 2156.972 391.8803 2526.386
## 2005.7781 1459.754 761.3747 2158.133 391.6751 2527.833
## 2005.7808 1457.696 758.7777 2156.615 388.7925 2526.600
## 2005.7836 1457.920 758.4622 2157.378 388.1916 2527.648
## 2005.7863 1450.966 750.9695 2150.962 380.4138 2521.518
## 2005.7890 1465.022 764.4877 2165.557 393.6471 2536.398
## 2005.7918 1479.180 778.1076 2180.253 406.9823 2551.378
## 2005.7945 1479.152 777.5420 2180.762 406.1322 2552.172
## 2005.7973 1476.709 774.5625 2178.856 402.8684 2550.550
## 2005.8000 1465.652 762.9687 2168.336 390.9905 2540.314
## 2005.8027 1458.371 755.1516 2161.591 382.8896 2533.853
## 2005.8055 1470.220 766.4646 2173.976 393.9189 2546.521
## 2005.8082 1471.542 767.2516 2175.833 394.4226 2548.662
## 2005.8110 1465.537 760.7115 2170.363 387.5993 2543.475
## 2005.8137 1433.762 728.4017 2139.123 355.0065 2512.518
## 2005.8164 1434.567 728.6724 2140.462 354.9944 2514.140
## 2005.8192 1440.625 734.1962 2147.053 360.2356 2521.013
## 2005.8219 1423.006 716.0444 2129.968 341.8015 2504.211
## 2005.8247 1450.604 743.1096 2158.099 368.5846 2532.624
## 2005.8274 1445.589 737.5618 2153.616 362.7548 2528.423
## 2005.8301 1440.754 732.1948 2149.314 357.1062 2524.402
## 2005.8329 1431.504 722.4129 2140.595 347.0428 2515.965
## 2005.8356 1439.339 729.7166 2148.961 354.0651 2524.613
## 2005.8384 1441.028 730.8746 2151.181 354.9421 2527.114
## 2005.8411 1427.367 716.6830 2138.051 340.4697 2514.264
## 2005.8438 1437.166 725.9520 2148.380 349.4580 2524.874
## 2005.8466 1449.232 737.4884 2160.976 360.7139 2537.751
## 2005.8493 1456.815 744.5419 2169.088 367.4872 2546.143
## 2005.8521 1464.004 751.2022 2176.807 373.8674 2554.141
## 2005.8548 1448.065 734.7345 2161.396 357.1200 2539.011
## 2005.8575 1450.877 737.0181 2164.736 359.1239 2542.630
## 2005.8603 1426.889 712.5020 2141.276 334.3284 2519.449
## 2005.8630 1408.953 694.0387 2123.867 315.5860 2502.320
## 2005.8658 1407.753 692.3119 2123.194 313.5801 2501.926
## 2005.8685 1413.682 697.7139 2129.650 318.7033 2508.660
## 2005.8712 1427.769 711.2747 2144.263 331.9856 2523.552
## 2005.8740 1434.426 717.4061 2151.446 337.8386 2531.014
## 2005.8767 1431.729 714.1838 2149.275 334.3382 2529.121
## 2005.8795 1430.955 712.8844 2149.026 332.7608 2529.149
## 2005.8822 1438.667 720.0720 2157.263 339.6706 2537.664
## 2005.8849 1438.769 719.6494 2157.889 338.9704 2538.568
## 2005.8877 1432.008 712.3645 2151.652 331.4082 2532.608
## 2005.8904 1424.278 704.1106 2144.445 322.8771 2525.678
## 2005.8932 1440.524 719.8335 2161.214 338.3230 2542.725
## 2005.8959 1439.810 718.5973 2161.024 336.8101 2542.811
## 2005.8986 1435.734 713.9987 2157.470 331.9350 2539.534
## 2005.9014 1431.617 709.3598 2153.875 327.0197 2536.215
## 2005.9041 1435.508 712.7284 2158.287 330.1122 2540.903
## 2005.9068 1425.497 702.1962 2148.797 319.3039 2531.690
## 2005.9096 1428.884 705.0627 2152.706 321.8948 2535.874
## 2005.9123 1429.754 705.4121 2154.096 321.9685 2537.540
## 2005.9151 1409.446 684.5835 2134.308 300.8646 2518.027
## 2005.9178 1410.066 684.6836 2135.448 300.6895 2519.442
## 2005.9205 1416.981 691.0798 2142.883 306.8108 2527.152
## 2005.9233 1424.422 698.0012 2150.842 313.4574 2535.386
## 2005.9260 1436.617 709.6779 2163.556 324.8595 2548.375
## 2005.9288 1431.448 703.9907 2158.906 318.8979 2543.999
## 2005.9315 1422.210 694.2341 2150.185 308.8672 2535.552
## 2005.9342 1439.264 710.7712 2167.757 325.1303 2553.398
## 2005.9370 1439.193 710.1832 2168.204 324.2684 2554.119
## 2005.9397 1435.640 706.1130 2165.167 319.9247 2551.356
## 2005.9425 1429.844 699.8006 2159.888 313.3388 2546.350
## 2005.9452 1441.651 711.0914 2172.211 324.3564 2558.946
## 2005.9479 1433.576 702.5008 2164.652 315.4928 2551.660
## 2005.9507 1434.063 702.4722 2165.654 315.1914 2552.935
## 2005.9534 1439.288 707.1822 2171.394 319.6288 2558.947
## 2005.9562 1425.715 693.0944 2158.336 305.2685 2546.161
## 2005.9589 1435.498 702.3635 2168.633 314.2654 2556.731
## 2005.9616 1437.877 704.2286 2171.526 315.8584 2559.896
## 2005.9644 1428.158 693.9955 2162.320 305.3534 2550.962
## 2005.9671 1424.275 689.5992 2158.950 300.6855 2547.864
## 2005.9699 1440.429 705.2410 2175.618 316.0557 2564.803
## 2005.9726 1448.327 712.6257 2184.028 323.1692 2573.484
## 2005.9753 1445.385 709.1716 2181.598 319.4439 2571.326
## 2005.9781 1441.604 704.8789 2178.329 314.8803 2568.327
## 2005.9808 1423.688 686.4520 2160.925 296.1826 2551.194
## 2005.9836 1414.803 677.0556 2152.550 286.5157 2543.090
## 2005.9863 1410.359 672.1010 2148.617 281.2907 2539.428
## 2005.9890 1409.275 670.5063 2148.043 279.4259 2539.124
## 2005.9918 1423.595 684.3168 2162.874 292.9663 2554.224
## 2005.9945 1430.756 690.9678 2170.544 299.3475 2562.164
## 2005.9973 1446.112 705.8147 2186.410 313.9248 2578.300
## 2006.0000 1443.563 702.7563 2184.369 310.5970 2576.529
## 2006.0027 1445.544 704.2286 2186.859 311.8001 2579.287
## 2006.0055 1445.009 703.1856 2186.832 310.4880 2579.530##NOTE: AIC = 30316.22 , BIC = 30333.30, RMSE = 21.41649 Also, the headline of the plot below contains ETS(A,N,N) showing that the automated model characterized error of the “tsWSR_PK” SERIES as Additative (A), trend as None (A) and seasonality as None (N) which is equivalent to simple exponential model(ses) with only alpha parameter i.e level.
#Model 2 : ARIMA Model It is used for forecasting for both seasonal and non- seasonal level.
#Changing to stationary set
train.sta_Var6 <- diff(train5, diff = 1)
test.sta_Var6 <- diff(test5, diff = 1)#2.1 Auto Arima model without sesonality:
set.seed(301)
model_Var6 <- auto.arima(train.sta_Var6, seasonal = FALSE)
summary(model_Var6)## Series: train.sta_Var6
## ARIMA(3,0,2) with zero mean
##
## Coefficients:
## ar1 ar2 ar3 ma1 ma2
## 0.6344 -0.1583 -0.0120 -0.5604 -0.3554
## s.e. 0.1744 0.1663 0.0809 0.1730 0.1549
##
## sigma^2 estimated as 446.8: log likelihood=-9796.41
## AIC=19604.82 AICc=19604.86 BIC=19638.98
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -0.09803186 21.11353 15.43441 NaN Inf 0.611181 0.001284281##NOTE: AIC = 19604.82 , BIC = 19638.98, RMSE = 21.11353
tsdisplay(residuals(model_Var6), lag.max = 45, main = '(1,1,1) Model Residuals')
#2.2 Auto Arima model with sesonality:
set.seed(301)
model2_Var6 <- auto.arima(train.sta_Var6, seasonal= TRUE)
summary(model2_Var6)## Series: train.sta_Var6
## ARIMA(5,0,3) with non-zero mean
##
## Coefficients:
## ar1 ar2 ar3 ar4 ar5 ma1 ma2 ma3
## 1.0352 -1.4682 1.1148 -0.5114 0.1458 -0.9648 0.9414 -0.8794
## s.e. 0.0732 0.0785 0.0660 0.0343 0.0258 0.0703 0.0722 0.0500
## mean
## 0.0057
## s.e. 0.0647
##
## sigma^2 estimated as 447: log likelihood=-9795.05
## AIC=19610.11 AICc=19610.21 BIC=19667.03
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -0.1292709 21.10002 15.42817 NaN Inf 0.6109338 0.003444275##NOTE: AIC = 19610.11 , BIC = 19667.03, RMSE = 21.10002
tsdisplay(residuals(model2_Var6), lag.max = 20, main = 'Seasonal Model Residuals')
NOTE: Above Graphs shows no serious lags.
#Plotting forecast for each model
fit_auto_train_Var6 %>% forecast(h=341) %>% autoplot() 
model2_Var6 %>% forecast(h=341) %>% autoplot() 
model_Var6 %>% forecast(h=341) %>% autoplot() 
COMMENT:
1. The plots includes 80% to 95% confidence interval.
2. For ARIMA models it plots the forecast but because of the nature of autoregressive process of 1 lag i.e. AR1, these forecast stabilizes quite smoothly.
Plot and comment on the residuals of the fitted data for both models in the same plot.
Residual Plot - to confirm no problem with this model
par(mfrow=c(1,3))
hist(fit_auto_train_Var6$residuals,col = 'red',xlab = 'Error',main = 'Histogram Of Residuals',freq= FALSE)
lines(density(fit_auto_train_Var6$residuals))
hist(model_Var6$residuals,col = 'red',xlab = 'Error',main = 'Histogram Of Residuals',freq= FALSE)
lines(density(model_Var6$residuals))
hist(model2_Var6$residuals,col = 'red',xlab = 'Error',main = 'Histogram Of Residuals',freq= FALSE)
lines(density(model2_Var6$residuals))
OBSERVATION: The residuals for each model are normally distributed, which shows the good fit of the models. It is normally distrbuted.
Testing the autocorrelation and partial autocorrelation of the residuals (using the plots and Ljung-Box Q statistic) up to an appropriate lag *
- ACF & PACF Plots
par(mfrow = c(3,2))
acf(fit_auto_train_Var6$residuals, main = 'Correlogram')
pacf(fit_auto_train_Var6$residuals, main = 'Partial Corelogram')
acf(model_Var6$residuals, main = 'Correlogram')
pacf(model_Var6$residuals, main = 'Partial Corelogram')
acf(model2_Var6$residuals, main = 'Correlogram')
pacf(model2_Var6$residuals, main = 'Partial Corelogram')
NOTE:
1. Residuals are the difference between actaual and fitted values
2. These blue lines are signficance bounds
3. This graph shows us the autocorelations for insample forecast errors
4. Do not exceed these significance bounds for lags 1 to end
- Ljunx-Box Test to check the autocorelations of the residuals
HO: No serial correlation upto 20 lags (does not exhibit lack of fit of the model)
Ha: Serial corelation is present (the model exhibits lack of fit)
We reject the null hypothesis, if p value is less than 0.05. This test is generally done for ARIMA models
Box.test(model_Var6$residuals, lag =20, type = 'Ljung-Box')##
## Box-Ljung test
##
## data: model_Var6$residuals
## X-squared = 17.219, df = 20, p-value = 0.6387Box.test(model2_Var6$residuals, lag =20, type = 'Ljung-Box')##
## Box-Ljung test
##
## data: model2_Var6$residuals
## X-squared = 16.943, df = 20, p-value = 0.6567OBSERVATIONS: For above performed Ljunx-Box Test on both the ARIMA models output, we can say that p-value is more than significance level 0.05, then there is not a statistical significance.
We conclude that there is a little evidence of non-zero auto-corelations in the insample forecast errors at lags 1 to 20.
So we fail to rejects the null hypothesis. Hence, we conclude that there is no serial auto corelation present between lags. Hence, the model seems to be good fit.
Test and comment on the normality of the residuals.
Here, further testing the normality by plotting Normal Q-Q plots. From below plots we observed that most of the datapoints lies on the line. Hence, we could conclude that our model produces residuals that are normal
par(mfrow = c(2,2))
qqnorm(fit_auto_train_Var6$residuals)
qqnorm(model_Var6$residuals)
qqnorm(model2_Var6$residuals)
Validating The Model by testing the model performance with Holdout set
Here, choosing RMSE as evaluation parameter. The lower RMSE indicates a more accurate forecast.
Below, is the comparison of model. We are fitting the model to test set which is the holdout set. And checking the accuracy using RMSE(Root mean square error) evaluation parameter.
accuracy(forecast(fit_auto_train_Var6), test5) ["Test set", "RMSE"]## [1] 103.0419#o/p - 103.0419
accuracy(forecast(model2_Var6), test.sta_Var6) ["Test set", "RMSE"]## [1] 23.82281#o/p -23.82281
accuracy(forecast(model_Var6), test.sta_Var6) ["Test set", "RMSE"]## [1] 23.86577#O/P - 23.86577
NOTE:- Here, the RMSE value is less of ARIMA models compared to exponential model.
The minimum RMSE is of model2_Var6
COMMENT ON BEST MODEL AND ITS PARAMETERS
We observed the best model to be ARIMA model i.e.“model2_Var6”.
summary(model2_Var6)## Series: train.sta_Var6
## ARIMA(5,0,3) with non-zero mean
##
## Coefficients:
## ar1 ar2 ar3 ar4 ar5 ma1 ma2 ma3
## 1.0352 -1.4682 1.1148 -0.5114 0.1458 -0.9648 0.9414 -0.8794
## s.e. 0.0732 0.0785 0.0660 0.0343 0.0258 0.0703 0.0722 0.0500
## mean
## 0.0057
## s.e. 0.0647
##
## sigma^2 estimated as 447: log likelihood=-9795.05
## AIC=19610.11 AICc=19610.21 BIC=19667.03
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -0.1292709 21.10002 15.42817 NaN Inf 0.6109338 0.003444275Passing parameter order = (5,0,3) ,which means
p = 5
d = 0
q = 3 <br.
For the best model, 5 member of lag is used as a predictor. As we transformed the series to stationary so members of differences needed for stationarity is 0. 3 are the number of lagged forecasts errors used in the prediction equation.
AIC = 19610.11, RMSE = 21.10002 which is minimum as compared to other models.
7. Forecasting on T at 700 hpa level (roughly 3100 m height)
#Checking the attributes of time series
attributes(tsT70)## $tsp
## [1] 1998.00 2004.94 365.00
##
## $class
## [1] "ts"#Plotting the series
plot(tsT70, main = "T at 700 hpa level (roughly 3100 m height)(tsT70)", col = "red")
From the plot, we observes that there seems to be no trend but seems to have seasonlity.
Checking the statistics and visualising the missing data in the series:
#Visualizing the series with missing data
plotNA.distribution(tsT70)
As we see the data is missing randomly, so locf and NOCB seems the good technique to implement here.
#Impute the missing values with “na_locf” function of “imputeTS package” and visualise the imputed values in the time series
tsT70.imp <- na_locf(tsT70)
plotNA.imputations(tsT70, tsT70.imp)
#Decomposition Of Time Series
decomp6 <- decompose(tsT70.imp)
plot(decomp6, col = "red")
OBSERVATIONS:
1)There does seems to have trend.
2) We observe the downward trend from year 1999 to 2002.
2)We observe some seasonality in the series. Seasonality describes cyclical effects due to the time of the year.
Let’s explore this seasonality pattern by plotting the decomp$seasonal components such that y-axis represents Seasonality Index and x-axis has month
plot(decomp6$seasonal[1:365], type ='b', xlab = 'Years', ylab = 'Seasonality Index', col = 'blue', las = 2, main = "SEASONAL DATA")
OBSERVATIONS:
1) There is increase in T for mid month of the year
2) There is a huge drop of T for starting and end months of the year
#Stationarity check of time series
We could check the stationarity of time series by ADF and KPSS Tests:
- Augmented Dickey- Fuller(ADF) t-statistic test for unit root
- Kwiatkowski-Phillips-Schmidt-Shin (KPSS) for level or trend stationarity
adf.test(tsT70.imp)## Warning in adf.test(tsT70.imp): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: tsT70.imp
## Dickey-Fuller = -5.8629, Lag order = 13, p-value = 0.01
## alternative hypothesis: stationary##p values is small, hence it is stationary
kpss.test(tsT70.imp, null="Trend")##
## KPSS Test for Trend Stationarity
##
## data: tsT70.imp
## KPSS Trend = 0.14889, Truncation lag parameter = 8, p-value = 0.0476##p - value is smaller than 0.05, hence it is not stationary
NOTE: From the both tests results, it leads to CASE4, we could recheck by visualising it i.e. by plotting ACF. Second, we can check each for characteristics of stationarity by looking at the autocorrelation functions (ACF) of each signal. For a stationary signal, because we expect no dependence with time, we would expect the ACF to go to 0 for each time lag (τ). Lets visualize the signals and ACFs.
Plotting ACF to check the auto-corelations
#Autocorelation plot
acf(tsT70.imp,lag.max = length(tsT70.imp),xlab = "lag #", ylab = 'ACF',main='Statiionary Check ')
Here, we observes most of the data lies outside the blue-dotted lines means the significance level. Now, we will take the difference to make our data stationary.
It seems difference of 1 is sufficient to make the series stationary.
tsT70.sta <- diff(tsT70.imp)
acf(tsT70.sta, lag.max = length(tsT70.sta),xlab = "lag #", ylab = 'ACF',main='Statiionary Check ')
Hence, after differencing our series is now transformed to stationary time series.
#Visualising the stationary series
plot(tsT70.sta, col = "red")
#CREATING MODELS AND FORECASTING: USING EXPONENTIAL SMOOTHING AND ARIMA TECHNIQUES FOR TIME SERIES FORECASTING
- TRAIN- TEST SET SPLIT
train6 <- window(tsT70.imp, end = c(2004, 3))
test6 <- window(tsT70.imp, start = c(2004, 4))#Model 1 : Auto Exponential Smoothening Model
set.seed(301)
fit_auto_train_Var7 <- forecast(train6)
summary(fit_auto_train_Var7)##
## Forecast method: STL + ETS(A,N,N)
##
## Model Information:
## ETS(A,N,N)
##
## Call:
## ets(y = na.interp(x), model = etsmodel, allow.multiplicative.trend = allow.multiplicative.trend)
##
## Smoothing parameters:
## alpha = 0.8894
##
## Initial states:
## l = 1.6601
##
## sigma: 1.9024
##
## AIC AICc BIC
## 19695.46 19695.47 19712.54
##
## Error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 0.002704966 1.901511 1.372217 -Inf Inf 0.4590085 0.0204421
##
## Forecasts:
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 2004.0082 3.4821134 1.0441172 5.920110 -0.246480 7.210707
## 2004.0110 2.5256287 -0.7370804 5.788338 -2.464254 7.515512
## 2004.0137 3.7585876 -0.1589008 7.676076 -2.232694 9.749869
## 2004.0164 4.3457573 -0.1317598 8.823274 -2.502014 11.193529
## 2004.0192 3.0227924 -1.9521050 7.997690 -4.585657 10.631242
## 2004.0219 2.3156617 -3.1112205 7.742544 -5.984038 10.615362
## 2004.0247 2.0293226 -3.8146909 7.873336 -6.908325 10.966970
## 2004.0274 4.3840559 -1.8492369 10.617349 -5.148943 13.917055
## 2004.0301 3.9698667 -2.6297836 10.569517 -6.123427 14.063161
## 2004.0329 3.9225818 -3.0241318 10.869295 -6.701500 14.546663
## 2004.0356 2.7692547 -4.5079889 10.046498 -8.360329 13.898838
## 2004.0384 3.6508231 -3.9425765 11.244223 -7.962280 15.263926
## 2004.0411 4.1913478 -3.7055607 12.088256 -7.885932 16.268627
## 2004.0438 4.1592460 -4.0299303 12.348422 -8.365018 16.683510
## 2004.0466 2.5934602 -5.8779064 11.064827 -10.362377 15.549298
## 2004.0493 3.0443987 -5.7000565 11.788854 -10.329092 16.417889
## 2004.0521 3.8863377 -5.1229321 12.895608 -9.892151 17.664827
## 2004.0548 2.6903773 -6.5761425 11.956897 -11.481542 16.862296
## 2004.0575 4.4038388 -5.1129796 13.920657 -10.150879 18.958557
## 2004.0603 3.0452195 -6.7154812 12.805920 -11.882484 17.972923
## 2004.0630 4.1639170 -5.8347190 14.162553 -11.127677 19.455511
## 2004.0658 4.4651485 -5.7658909 14.696188 -11.181876 20.112173
## 2004.0685 2.1753740 -8.2829056 12.633654 -13.819184 18.169932
## 2004.0712 3.2040254 -7.4766607 13.884712 -13.130674 19.538725
## 2004.0740 5.5271570 -5.3713980 16.425712 -11.140745 22.195059
## 2004.0767 4.9326012 -6.1795519 16.044754 -12.061970 21.927173
## 2004.0795 3.6140902 -7.7076319 14.935812 -13.700990 20.929170
## 2004.0822 4.9626588 -6.5648229 16.490141 -12.667103 22.592421
## 2004.0849 5.0456011 -6.6840315 16.775234 -12.893324 22.984526
## 2004.0877 4.4338014 -7.4945567 16.362159 -13.809048 22.676651
## 2004.0904 5.2382856 -6.8855410 17.362112 -13.303507 23.780078
## 2004.0932 4.1948368 -8.1213564 16.511030 -14.641155 23.030829
## 2004.0959 4.4865970 -8.0190042 16.992198 -14.639070 23.612263
## 2004.0986 4.1856260 -8.5065568 16.877809 -15.225393 23.596645
## 2004.1014 5.3155821 -7.5604790 18.191643 -14.376654 25.007818
## 2004.1041 4.2831154 -8.7742348 17.340466 -15.686378 24.252609
## 2004.1068 4.2824310 -8.9537255 17.518588 -15.960524 24.525386
## 2004.1096 2.1809636 -11.2316157 15.593543 -18.331806 22.693734
## 2004.1123 3.3111259 -10.2755856 16.897837 -17.467956 24.090208
## 2004.1151 4.9874704 -8.7711696 18.746110 -16.054554 26.029494
## 2004.1178 5.2870935 -8.6413529 19.215540 -16.014627 26.588814
## 2004.1205 4.3670994 -9.7291080 18.463307 -17.191189 25.925388
## 2004.1233 3.8979611 -10.3640341 18.159956 -17.913878 25.709801
## 2004.1260 3.5132505 -10.9126274 17.939128 -18.549226 25.575727
## 2004.1288 4.0474341 -10.5404855 18.635354 -18.262864 26.357732
## 2004.1315 4.7928847 -9.9552964 19.541066 -17.762512 27.348281
## 2004.1342 4.2468832 -10.6598363 19.153603 -18.550977 27.044743
## 2004.1370 0.9770956 -14.0864940 16.040685 -22.060677 24.014868
## 2004.1397 2.8484039 -12.3704390 18.067247 -20.426808 26.123615
## 2004.1425 3.3846878 -11.9878404 18.757216 -20.125565 26.894941
## 2004.1452 3.6441420 -11.8805501 19.168834 -20.098826 27.387110
## 2004.1479 4.8681392 -10.8072399 20.543518 -19.105284 28.841563
## 2004.1507 4.3069849 -11.5176464 20.131616 -19.894700 28.508670
## 2004.1534 3.7691741 -12.2033148 19.741663 -20.658640 28.196988
## 2004.1562 2.5930154 -13.5259749 18.712006 -22.058853 27.244884
## 2004.1589 2.4611128 -13.8030592 18.725285 -22.412792 27.335017
## 2004.1616 4.5474117 -11.8606576 20.955481 -20.546565 29.641388
## 2004.1644 2.7180617 -13.8326537 19.268777 -22.594073 28.030197
## 2004.1671 4.5195432 -12.1725994 21.211686 -21.008886 30.047972
## 2004.1699 5.7783941 -11.0539875 22.610776 -19.964512 31.521300
## 2004.1726 5.4957186 -11.4757432 22.467180 -20.459892 31.451330
## 2004.1753 5.1143727 -11.9950388 22.223784 -21.052214 31.280959
## 2004.1781 5.4635696 -11.7826881 22.709827 -20.912305 31.839445
## 2004.1808 2.3467987 -15.0352279 19.728825 -24.236717 28.930314
## 2004.1836 2.0917731 -15.4249701 19.608516 -24.697774 28.881320
## 2004.1863 1.1602201 -16.4902116 18.810652 -25.833786 28.154226
## 2004.1890 4.5096232 -13.2734920 22.292738 -22.687304 31.706551
## 2004.1918 5.9831642 -11.9316517 23.897980 -21.415182 33.381511
## 2004.1945 6.3254152 -11.7201403 24.370971 -21.272880 33.923711
## 2004.1973 4.7334749 -13.4418798 22.908830 -23.063331 32.530281
## 2004.2000 4.0451410 -14.2590925 22.349375 -23.948768 32.039050
## 2004.2027 4.9730091 -13.4592020 23.405220 -23.216625 33.162644
## 2004.2055 6.5103089 -12.0489975 25.069615 -21.873701 34.894319
## 2004.2082 6.2915953 -12.3939419 24.977132 -22.285468 34.868658
## 2004.2110 3.5892818 -15.2216390 22.400203 -25.179539 32.358103
## 2004.2137 4.9373643 -13.9981100 23.872839 -24.021945 33.896673
## 2004.2164 5.7682546 -13.2909593 24.827468 -23.380298 34.916807
## 2004.2192 5.9599906 -13.2221646 25.142146 -23.376584 35.296565
## 2004.2219 3.9184128 -15.3859008 23.222726 -25.604987 33.441813
## 2004.2247 5.4870188 -13.9386849 24.912723 -24.222031 35.196069
## 2004.2274 6.5354177 -13.0109225 26.081758 -23.358130 36.428965
## 2004.2301 6.4289092 -13.2373273 26.095146 -23.648004 36.505822
## 2004.2329 8.0451317 -11.7402746 27.830538 -22.214036 38.304299
## 2004.2356 8.5012418 -11.4026208 28.405104 -21.939089 38.941573
## 2004.2384 9.4622148 -10.5594033 29.483833 -21.158208 40.082637
## 2004.2411 8.8449054 -11.2937796 28.983591 -21.954556 39.644366
## 2004.2438 6.7650464 -13.4900291 27.020122 -24.212418 37.742511
## 2004.2466 7.4315769 -12.9392240 27.802378 -23.722875 38.586028
## 2004.2493 7.3183509 -13.1675215 27.804223 -24.012087 38.648789
## 2004.2521 8.8912614 -11.7090400 29.491563 -22.614181 40.396704
## 2004.2548 8.7565501 -11.9575480 29.470648 -22.922929 40.436029
## 2004.2575 8.4205126 -12.4067605 29.247786 -23.432053 40.273078
## 2004.2603 7.1952933 -13.7445432 28.135130 -24.829423 39.220010
## 2004.2630 8.8721698 -12.1796282 29.923968 -23.323777 41.068116
## 2004.2658 9.8584377 -11.3047293 31.021605 -22.507833 42.224709
## 2004.2685 10.2399790 -11.0339742 31.513932 -22.295725 42.775683
## 2004.2712 8.9237045 -12.4604609 30.307870 -23.780554 41.627963
## 2004.2740 8.5458797 -12.9479328 30.039692 -24.326070 41.417829
## 2004.2767 6.9993236 -14.6035795 28.602227 -26.039466 40.038113
## 2004.2795 6.3824239 -15.3290216 28.093869 -26.822367 39.587214
## 2004.2822 7.4904390 -14.3290089 29.309887 -25.879527 40.860405
## 2004.2849 8.5990955 -13.3278230 30.526014 -24.935232 42.133423
## 2004.2877 8.4638796 -13.5699852 30.497744 -25.234009 42.161768
## 2004.2904 9.8294611 -12.3108335 31.969756 -24.031197 43.690120
## 2004.2932 10.2541953 -11.9920199 32.500410 -23.768455 44.276845
## 2004.2959 9.8972717 -12.4543621 32.248905 -24.286602 44.081146
## 2004.2986 8.9201787 -13.5363789 31.376736 -25.424162 43.264520
## 2004.3014 7.8102626 -14.7507308 30.371256 -26.693799 42.314324
## 2004.3041 6.8926315 -15.7723165 29.557579 -27.770415 41.555678
## 2004.3068 7.6653450 -15.1030830 30.433773 -27.155961 42.486651
## 2004.3096 8.1789631 -14.6924767 31.050403 -26.799886 43.157812
## 2004.3123 9.2212045 -13.7527852 32.195194 -25.914481 44.356890
## 2004.3151 9.0340546 -14.0420293 32.110138 -26.257770 44.325879
## 2004.3178 9.0605773 -14.1171511 32.238306 -26.386699 44.507854
## 2004.3205 8.7228710 -14.5560581 32.001800 -26.879179 44.324921
## 2004.3233 9.5554062 -13.8242854 32.935098 -26.200747 45.311559
## 2004.3260 9.1572267 -14.3227951 32.637249 -26.752368 45.066821
## 2004.3288 7.5535666 -16.0263586 31.133492 -28.508817 43.615950
## 2004.3315 6.9332012 -16.7462058 30.612608 -29.281327 43.147729
## 2004.3342 7.1178009 -16.6606718 30.896274 -29.248235 43.483837
## 2004.3370 8.7953890 -15.0817383 32.672516 -27.721526 45.312304
## 2004.3397 9.0849602 -14.8904157 33.060336 -27.582213 45.752133
## 2004.3425 8.7332752 -15.3399485 32.806499 -28.083543 45.550094
## 2004.3452 9.2313540 -14.9393212 33.402029 -27.734504 46.197212
## 2004.3479 9.0852825 -15.1824530 33.353018 -28.029016 46.199581
## 2004.3507 9.3764745 -14.9879346 33.740884 -27.885674 46.638623
## 2004.3534 9.5793047 -14.8813959 34.040005 -27.830109 46.988718
## 2004.3562 8.8195702 -15.7370444 33.376185 -28.736531 46.375671
## 2004.3589 10.1059410 -14.5462143 34.758096 -27.596277 47.808159
## 2004.3616 9.6015698 -15.1457575 34.348897 -28.246201 47.449341
## 2004.3644 9.0110857 -15.8310489 33.853220 -28.981681 47.003852
## 2004.3671 8.5061213 -16.4304603 33.442703 -29.631089 46.643332
## 2004.3699 8.9143140 -16.1163581 33.944986 -29.366795 47.195423
## 2004.3726 9.6320787 -15.4923315 34.756489 -28.792391 48.056548
## 2004.3753 9.8683409 -15.3494590 35.086141 -28.698956 48.435638
## 2004.3781 8.8422073 -16.4686378 34.153052 -29.867390 47.551804
## 2004.3808 9.6363068 -15.7672426 35.039856 -29.215069 48.487683
## 2004.3836 10.0362880 -15.4596287 35.532205 -28.956352 49.028928
## 2004.3863 9.9514910 -15.6364595 35.539442 -29.181902 49.084884
## 2004.3890 9.6098406 -16.0698140 35.289495 -29.663802 48.883483
## 2004.3918 8.3577870 -17.4132452 34.128819 -31.055606 47.771180
## 2004.3945 8.4181658 -17.4439213 34.280253 -31.134483 47.970815
## 2004.3973 8.8443519 -17.1084706 34.797174 -30.847065 48.535769
## 2004.4000 9.2091634 -16.8340783 35.252405 -30.620538 49.038864
## 2004.4027 9.8409131 -16.2924350 35.974261 -30.126594 49.808420
## 2004.4055 9.6744978 -16.5486471 35.897643 -30.430341 49.779337
## 2004.4082 9.6301029 -16.6825323 35.942738 -30.611600 49.871806
## 2004.4110 10.9915218 -15.4103004 37.393344 -29.386581 51.369624
## 2004.4137 10.4781057 -16.0126033 36.968815 -30.035938 50.992149
## 2004.4164 10.2786718 -16.3006266 36.857970 -30.370857 50.928201
## 2004.4192 10.2211904 -16.4464032 36.888784 -30.563375 51.005755
## 2004.4219 9.5005260 -17.2550715 36.256123 -31.418629 50.419681
## 2004.4247 9.6324162 -17.2108966 36.475729 -31.420888 50.685720
## 2004.4274 9.4938697 -17.4368727 36.424612 -31.693147 50.680886
## 2004.4301 8.6067546 -18.4111345 35.624644 -32.713541 49.927050
## 2004.4329 8.8864575 -18.2182980 35.991213 -32.566689 50.339604
## 2004.4356 9.0560002 -18.1353444 36.247345 -32.529573 50.641573
## 2004.4384 9.3078080 -17.9698507 36.585467 -32.409771 51.025387
## 2004.4411 8.3679678 -18.9957328 35.731668 -33.481201 50.217136
## 2004.4438 9.3940601 -18.0554127 36.843533 -32.586286 51.374406
## 2004.4466 9.1995329 -18.3354449 36.734511 -32.911582 51.310647
## 2004.4493 8.9756158 -18.6446022 36.595834 -33.265862 51.217094
## 2004.4521 8.6017445 -19.1034516 36.306941 -33.769696 50.973185
## 2004.4548 8.6920610 -19.0978533 36.481975 -33.808945 51.193067
## 2004.4575 8.8703828 -19.0039922 36.744758 -33.759795 51.500560
## 2004.4603 8.5144784 -19.4441021 36.473059 -34.244481 51.273437
## 2004.4630 9.1506087 -18.8919245 37.193142 -33.736745 52.037962
## 2004.4658 9.0227440 -19.1034913 37.148979 -33.992621 52.038109
## 2004.4685 9.1610218 -19.0486673 37.370711 -33.981975 52.304018
## 2004.4712 9.9443191 -18.3485776 38.237216 -33.325932 53.214571
## 2004.4740 10.1849243 -18.1909360 38.560785 -33.212209 53.582058
## 2004.4767 9.8216771 -18.6369050 38.280259 -33.701968 53.345322
## 2004.4795 10.2126839 -18.3283801 38.753748 -33.437107 53.862475
## 2004.4822 10.2317930 -18.3915153 38.855101 -33.543780 54.007366
## 2004.4849 9.8872820 -18.8180350 38.592599 -34.013712 53.788276
## 2004.4877 10.2421564 -18.5449357 39.029248 -33.783902 54.268215
## 2004.4904 10.2527978 -18.6158377 39.121433 -33.897970 54.403566
## 2004.4932 10.1538837 -18.7960655 39.103833 -34.121243 54.429010
## 2004.4959 10.2407475 -18.7902877 39.271783 -34.158389 54.639884
## 2004.4986 10.1650815 -18.9468139 39.276977 -34.357720 54.687883
## 2004.5014 10.1277208 -19.0648107 39.320252 -34.518403 54.773845
## 2004.5041 10.0705527 -19.2023929 39.343498 -34.698554 54.839660
## 2004.5068 10.5337643 -18.8193749 39.886904 -34.357988 55.425517
## 2004.5096 10.1784045 -19.2547101 39.611519 -34.835660 55.192469
## 2004.5123 10.2580593 -19.2548138 39.770932 -34.877985 55.394104
## 2004.5151 10.1565566 -19.4358600 39.748973 -35.101139 55.414252
## 2004.5178 10.1087691 -19.5629778 39.780516 -35.270252 55.487790
## 2004.5205 10.0362993 -19.7145664 39.787165 -35.463723 55.536322
## 2004.5233 9.6718450 -20.1579296 39.501620 -35.948858 55.292548
## 2004.5260 9.4063739 -20.5021015 39.314849 -36.334692 55.147440
## 2004.5288 9.3140676 -20.6729020 39.301037 -36.547045 55.175180
## 2004.5315 10.0602552 -20.0050037 40.125514 -35.920590 56.041101
## 2004.5342 10.6482731 -19.4950717 40.791618 -35.451995 56.748541
## 2004.5370 10.2382235 -19.9830055 40.459452 -35.981158 56.457605
## 2004.5397 9.9298008 -20.3691121 40.228714 -36.408388 56.267989
## 2004.5425 10.5654203 -19.8109779 40.941819 -35.891272 57.022112
## 2004.5452 10.7652659 -19.6884205 41.218952 -35.809628 57.340160
## 2004.5479 9.7845167 -20.7462621 40.315296 -36.908280 56.477314
## 2004.5507 9.0395213 -21.5681559 39.647198 -37.770882 55.849924
## 2004.5534 8.5537031 -22.1306797 39.238086 -38.374011 55.481417
## 2004.5562 8.9853516 -21.7755456 39.746249 -38.059381 56.030084
## 2004.5589 9.8705768 -20.9666448 40.707798 -37.290884 57.032037
## 2004.5616 9.6709696 -21.2423881 40.584327 -37.606931 56.948870
## 2004.5644 10.1361772 -20.8531294 41.125484 -37.257877 57.530232
## 2004.5671 10.2615480 -20.8035219 41.326618 -37.248377 57.771473
## 2004.5699 10.2924728 -20.8481761 41.433122 -37.333040 57.917986
## 2004.5726 10.2770604 -20.9389845 41.493105 -37.463761 58.017881
## 2004.5753 9.9876609 -21.3035983 41.278920 -37.868190 57.843512
## 2004.5781 10.4778448 -20.8884484 41.844138 -37.492761 58.448451
## 2004.5808 10.1663966 -21.2747515 41.607545 -37.918690 58.251483
## 2004.5836 10.5867371 -20.9290881 42.102562 -37.612558 58.786032
## 2004.5863 9.8003730 -21.7899529 41.390699 -38.512861 58.113607
## 2004.5890 10.1985698 -21.4660814 41.863221 -38.228335 58.625475
## 2004.5918 10.3443720 -21.3944303 42.083174 -38.195937 58.884681
## 2004.5945 10.4943412 -21.3184395 42.307122 -38.159108 59.147791
## 2004.5973 9.6246529 -22.2619346 41.511240 -39.141674 58.390980
## 2004.6000 9.7902271 -22.1699968 41.750451 -39.088717 58.669171
## 2004.6027 9.8565647 -22.1771262 41.890256 -39.134738 58.847867
## 2004.6055 9.9126685 -22.1943214 42.019658 -39.190735 59.016072
## 2004.6082 9.4206484 -22.7594735 41.600770 -39.794601 58.635898
## 2004.6110 10.2728857 -21.9802024 42.525974 -39.053956 59.599727
## 2004.6137 10.5400599 -21.7858296 42.865949 -38.898122 59.978242
## 2004.6164 10.2966706 -22.1018569 42.695198 -39.252601 59.845942
## 2004.6192 9.8083697 -22.6626331 42.279373 -39.851744 59.468483
## 2004.6219 9.5256661 -23.0176507 42.068983 -40.245042 59.296374
## 2004.6247 9.5814856 -23.0339849 42.196956 -40.299572 59.462543
## 2004.6274 9.6249647 -23.0625001 42.312430 -40.366199 59.616128
## 2004.6301 9.2277738 -23.5315272 41.987075 -40.873254 59.328801
## 2004.6329 9.6776200 -23.1533600 42.508600 -40.533031 59.888271
## 2004.6356 9.5081386 -23.3943642 42.410641 -40.811897 59.828174
## 2004.6384 9.6903988 -23.2834717 42.664269 -40.738784 60.119582
## 2004.6411 9.8481057 -23.1969784 42.893190 -40.689989 60.386201
## 2004.6438 9.8367696 -23.2793749 42.952914 -40.810003 60.483542
## 2004.6466 9.8976129 -23.2894399 43.084666 -40.857604 60.652830
## 2004.6493 9.4477551 -23.8100548 42.705565 -41.415676 60.311186
## 2004.6521 10.1127912 -23.2156255 43.441208 -40.858624 61.084206
## 2004.6548 10.5555863 -22.8432881 43.954461 -40.523584 61.634757
## 2004.6575 9.7489903 -23.7201933 43.218174 -41.437709 60.935689
## 2004.6603 9.9416990 -23.5976465 43.481045 -41.352304 61.235702
## 2004.6630 10.1479831 -23.4613778 43.757344 -41.253099 61.549065
## 2004.6658 9.5498076 -24.1294232 43.229038 -41.958131 61.057746
## 2004.6685 9.4137231 -24.3352329 43.162679 -42.200851 61.028297
## 2004.6712 9.6068129 -24.2117246 43.425350 -42.114177 61.327803
## 2004.6740 9.0548033 -24.8331728 42.942779 -42.772384 60.881990
## 2004.6767 9.5596205 -24.3976522 43.516893 -42.373546 61.492787
## 2004.6795 9.2925485 -24.7338796 43.318977 -42.746383 61.331480
## 2004.6822 9.4992808 -24.5961625 43.594724 -42.645200 61.643762
## 2004.6849 9.6608947 -24.5034244 43.825214 -42.588922 61.910712
## 2004.6877 9.2189491 -25.0141072 43.452005 -43.135993 61.573891
## 2004.6904 8.6059664 -25.6956894 42.907622 -43.853889 61.065822
## 2004.6932 9.7487220 -24.6213964 44.118840 -42.815838 62.313282
## 2004.6959 10.2562615 -24.1821833 44.694706 -42.412795 62.925318
## 2004.6986 10.5491299 -23.9575061 45.055766 -42.224216 63.322475
## 2004.7014 9.5014427 -25.0732500 44.076135 -43.375987 62.378872
## 2004.7041 9.7801473 -24.8624682 44.422763 -43.201161 62.761456
## 2004.7068 8.3193953 -26.3910104 43.029801 -44.765589 61.404380
## 2004.7096 7.4988943 -27.2791693 42.276958 -45.689564 60.687353
## 2004.7123 8.1464772 -26.6991129 42.992067 -45.145254 61.438208
## 2004.7151 9.1944363 -25.7185497 44.107422 -44.200368 62.589241
## 2004.7178 10.1383454 -24.8419068 45.118597 -43.359334 63.636024
## 2004.7205 10.4320637 -24.6153254 45.479453 -43.168293 64.032420
## 2004.7233 9.4879223 -25.6264755 44.602320 -44.214915 63.190759
## 2004.7260 8.7143604 -26.4669183 43.895639 -45.090762 62.519483
## 2004.7288 8.4976575 -26.7503754 43.745690 -45.409557 62.404872
## 2004.7315 7.8734705 -27.4411903 43.188131 -46.135642 61.882583
## 2004.7342 7.4479661 -27.9331970 42.829129 -46.662853 61.558786
## 2004.7370 7.7672379 -27.6803030 43.214779 -46.445098 61.979573
## 2004.7397 7.8308069 -27.6829875 43.344601 -46.482855 62.144469
## 2004.7425 6.6069307 -28.9729940 42.186855 -47.807868 61.021730
## 2004.7452 7.2208239 -28.4251084 42.866756 -47.294925 61.736573
## 2004.7479 8.4275325 -27.2842853 44.139350 -46.188980 63.044045
## 2004.7507 7.7589612 -28.0186208 43.536543 -46.958129 62.476051
## 2004.7534 8.1306220 -27.7126036 43.973848 -46.686861 62.948105
## 2004.7562 8.3014454 -27.6073037 44.210195 -46.616247 63.219138
## 2004.7589 6.5187261 -29.4554273 42.492879 -48.498994 61.536446
## 2004.7616 6.7839993 -29.2554396 42.823438 -48.333566 61.901565
## 2004.7644 7.3716476 -28.7329587 43.476254 -47.845583 62.588878
## 2004.7671 6.5046950 -29.6649614 42.674351 -48.812021 61.821411
## 2004.7699 7.7056608 -28.5289289 43.940250 -47.710362 63.121684
## 2004.7726 8.6912089 -27.6081979 44.990616 -46.823943 64.206361
## 2004.7753 8.6051797 -27.7589287 44.969288 -47.008925 64.219284
## 2004.7781 8.8776953 -27.5509997 45.306390 -46.835186 64.590577
## 2004.7808 8.3342666 -28.1589009 44.827434 -47.477217 64.145750
## 2004.7836 8.1834835 -28.3740426 44.741010 -47.726428 64.093395
## 2004.7863 7.1667784 -29.4549932 43.788550 -48.841388 63.174945
## 2004.7890 7.3760709 -29.3098338 44.061976 -48.730179 63.482320
## 2004.7918 7.4626871 -29.2872387 44.212613 -48.741474 63.666849
## 2004.7945 7.6513501 -29.1624856 44.465186 -48.650553 63.953253
## 2004.7973 6.8843199 -29.9933148 43.761955 -49.515155 63.283795
## 2004.8000 6.3360318 -30.6052917 43.277355 -50.160847 62.832911
## 2004.8027 7.6684639 -29.3364388 44.673367 -48.925651 64.262579
## 2004.8055 7.2126868 -29.8556861 44.281060 -49.478497 63.903871
## 2004.8082 6.7247170 -30.4070176 43.856452 -50.063371 63.512805
## 2004.8110 5.9564544 -31.2385341 43.151443 -50.928372 62.841280
## 2004.8137 6.8514132 -30.4067216 44.109548 -50.129987 63.832813
## 2004.8164 5.2032611 -32.1179132 42.524435 -51.874549 62.281072
## 2004.8192 4.5483747 -32.8357328 41.932482 -52.625684 61.722433
## 2004.8219 4.7023620 -32.7445730 42.149297 -52.567783 61.972507
## 2004.8247 6.1656495 -31.3440077 43.675307 -51.200421 63.531720
## 2004.8274 5.6057306 -31.9665441 43.178005 -51.856105 63.067566
## 2004.8301 5.0979558 -32.5368323 42.732744 -52.459486 62.655397
## 2004.8329 5.2180558 -32.4791420 42.915254 -52.434833 62.870945
## 2004.8356 4.4430907 -33.3164137 42.202595 -53.305088 62.191269
## 2004.8384 5.5972037 -32.2245045 43.418912 -52.246107 63.440515
## 2004.8411 5.4255543 -32.4582557 43.309364 -52.512733 63.363842
## 2004.8438 4.9948131 -32.9509970 42.940623 -53.038295 63.027922
## 2004.8466 4.7252441 -33.2824650 42.732953 -53.402531 62.853019
## 2004.8493 4.3867674 -33.6827399 42.456275 -53.835520 62.609055
## 2004.8521 4.5224429 -33.6087627 42.653648 -53.794204 62.839089
## 2004.8548 4.9704096 -33.2223944 43.163214 -53.440444 63.381263
## 2004.8575 4.2412825 -34.0130209 42.495586 -54.263626 62.746191
## 2004.8603 4.9185991 -33.3971048 43.234303 -53.680213 63.517412
## 2004.8630 4.8126553 -33.5643511 43.189662 -53.879911 63.505222
## 2004.8658 5.8985388 -32.5396721 44.336750 -52.887632 64.684709
## 2004.8685 3.4815656 -35.0177526 41.980884 -55.398061 62.361192
## 2004.8712 4.2936370 -34.2666917 42.853966 -54.679297 63.266571
## 2004.8740 5.1536441 -33.4675987 43.774887 -53.912450 64.219738
## 2004.8767 5.0986342 -33.5834268 43.780695 -54.060473 64.257741
## 2004.8795 3.4980516 -35.2447321 42.240835 -55.753923 62.750026
## 2004.8822 4.3913361 -34.4120752 43.194747 -54.953360 63.736033
## 2004.8849 4.8789595 -33.9849849 43.742904 -54.558314 64.316233
## 2004.8877 4.1923813 -34.7320021 43.116765 -55.337326 63.722088
## 2004.8904 2.1794616 -36.8052670 41.164190 -57.442536 61.801459
## 2004.8932 3.8463571 -35.1986235 42.891338 -55.867788 63.560502
## 2004.8959 4.2514796 -34.8536602 43.356619 -55.554671 64.057630
## 2004.8986 3.6108375 -35.5543689 42.776044 -56.287177 63.508852
## 2004.9014 6.3421416 -32.8830396 45.567323 -53.647596 66.331879
## 2004.9041 4.9167190 -34.3683454 44.201783 -55.164602 64.998040
## 2004.9068 4.4882731 -34.8565834 43.833130 -55.684492 64.661038
## 2004.9096 4.8616170 -34.5429408 44.266175 -55.402454 65.125688
## 2004.9123 5.2652872 -34.1988816 44.729456 -55.089951 65.620525
## 2004.9151 3.2647330 -36.2589570 42.788423 -57.181535 63.711001
## 2004.9178 4.1288065 -35.4543150 43.711928 -56.408354 64.665967
## 2004.9205 5.0326986 -34.6097654 44.675163 -55.595218 65.660616
## 2004.9233 2.9132172 -36.7885007 42.614935 -57.805321 63.631755
## 2004.9260 3.5113647 -36.2495187 43.272248 -57.297659 64.320388
## 2004.9288 4.4125137 -35.4074472 44.232475 -56.486861 65.311889
## 2004.9315 2.3753115 -37.5036396 42.254263 -58.614281 63.364904
## 2004.9342 3.8301764 -36.1076775 43.768030 -57.249500 64.909853
## 2004.9370 2.9886507 -37.0080195 42.985321 -58.180978 64.158279
## 2004.9397 1.4142790 -38.6411210 41.469679 -59.845169 62.673727
## 2004.9425 2.8681940 -37.2458499 42.982238 -58.480942 64.217330
## 2004.9452 3.6526821 -36.5199200 43.825284 -57.786011 65.091375
## 2004.9479 3.3844785 -36.8465966 43.615554 -58.143641 64.912598
## 2004.9507 1.6235840 -38.6658793 41.913047 -59.993833 63.241001
## 2004.9534 2.4069517 -37.9408152 42.754719 -59.299633 64.113536
## 2004.9562 0.8795863 -39.5264001 41.285573 -60.916037 62.675210
## 2004.9589 3.3722012 -37.0919210 43.836323 -58.512333 65.256736
## 2004.9616 2.5871211 -37.9350534 43.109296 -59.386197 64.560439
## 2004.9644 1.6026269 -38.9775169 42.182771 -60.459347 63.664601
## 2004.9671 1.2869734 -39.3510571 41.925004 -60.863531 63.437478
## 2004.9699 1.9267866 -38.7690482 42.622621 -60.312122 64.165695
## 2004.9726 0.1962828 -40.5572742 40.949840 -62.130904 62.523470
## 2004.9753 1.5884800 -39.2227177 42.399678 -60.826861 64.003821
## 2004.9781 3.2312324 -37.6375246 44.099989 -59.272138 65.734602
## 2004.9808 2.3686729 -38.5575624 43.294908 -60.222603 64.959949
## 2004.9836 2.0739974 -38.9096357 43.057631 -60.605061 64.753055
## 2004.9863 1.0336628 -40.0072878 42.074614 -61.733055 63.800380
## 2004.9890 -0.2355325 -41.3337208 40.862656 -63.089787 62.618722
## 2004.9918 1.7310214 -39.4243248 42.886368 -61.210649 64.672692
## 2004.9945 1.5290033 -39.6834216 42.741428 -61.499961 64.557968
## 2004.9973 1.2229817 -40.0464429 42.492406 -61.893157 64.339120
## 2005.0000 3.5028204 -37.8235254 44.829166 -59.700371 66.706012
## 2005.0027 2.5034075 -38.8797811 43.886596 -60.786718 65.793533
## 2005.0055 2.4826142 -38.9573393 43.922568 -60.894326 65.859554
## 2005.0082 3.4821134 -38.0145273 44.978754 -59.981522 66.945749
## 2005.0110 2.5256287 -39.0276219 44.078879 -61.024584 66.075841
## 2005.0137 3.7585876 -37.8511959 45.368371 -59.878085 67.395260
## 2005.0164 4.3457573 -37.3204823 46.011997 -59.377257 68.068772
## 2005.0192 3.0227924 -38.6998270 44.745412 -60.786448 66.832032
## 2005.0219 2.3156617 -39.4632614 44.094585 -61.579687 66.211011
## 2005.0247 2.0293226 -39.8058284 43.864474 -61.952020 66.010665
## 2005.0274 4.3840559 -37.5072475 46.275359 -59.683164 68.451276
## 2005.0301 3.9698667 -37.9775140 45.917247 -60.183116 68.122849
## 2005.0329 3.9225818 -38.0808014 45.925965 -60.316049 68.161213
## 2005.0356 2.7692547 -39.2900563 44.828566 -61.554911 67.093420
## 2005.0384 3.6508231 -38.4643414 45.765988 -60.758763 68.060409
## 2005.0411 4.1913478 -37.9795964 46.362292 -60.303546 68.686241
## 2005.0438 4.1592460 -38.0674041 46.385896 -60.420842 68.739334
## 2005.0466 2.5934602 -39.6888223 44.875743 -62.071711 67.258631
## 2005.0493 3.0443987 -39.2934433 45.382241 -61.705743 67.794540
## 2005.0521 3.8863377 -38.5069908 46.279666 -60.948663 68.721339
## 2005.0548 2.6903773 -39.7583654 45.139120 -62.229372 67.610127
## 2005.0575 4.4038388 -38.1002457 46.907923 -60.600549 69.408226
## 2005.0603 3.0452195 -39.5141349 45.604574 -62.043696 68.134135
## 2005.0630 4.1639170 -38.4506355 46.778470 -61.009417 69.337251
## 2005.0658 4.4651485 -38.2045308 47.134828 -60.792495 69.722792
## 2005.0685 2.1753740 -40.5493610 44.900109 -63.166469 67.517217
## 2005.0712 3.2040254 -39.5756943 45.983745 -62.221910 68.629961
## 2005.0740 5.5271570 -37.3074769 48.361791 -59.982762 71.037077
## 2005.0767 4.9326012 -37.9568767 47.822079 -60.661195 70.526397
## 2005.0795 3.6140902 -39.3301616 46.558342 -62.063475 69.291656
## 2005.0822 4.9626588 -38.0362970 47.961615 -60.798569 70.723887
## 2005.0849 5.0456011 -38.0079893 48.099191 -60.799183 70.890386
## 2005.0877 4.4338014 -38.6743543 47.541957 -61.494434 70.362036
## 2005.0904 5.2382856 -37.9243665 48.400938 -60.773294 71.249866
## 2005.0932 4.1948368 -39.0222429 47.411917 -61.899983 70.289657
## 2005.0959 4.4865970 -38.7848419 47.758036 -61.691358 70.664552
## 2005.0986 4.1856260 -39.1401039 47.511356 -62.075360 70.446612
## 2005.1014 5.3155821 -38.0643708 48.695535 -61.028331 71.659495
## 2005.1041 4.2831154 -39.1509928 47.717224 -62.143621 70.709852
## 2005.1068 4.2824310 -39.2057652 47.770627 -62.227026 70.791888
## 2005.1096 2.1809636 -41.3612533 45.723180 -64.411111 68.773038
## 2005.1123 3.3111259 -40.2850448 46.907297 -63.363463 69.985715
## 2005.1151 4.9874704 -38.6625873 48.637528 -61.769532 71.744473
## 2005.1178 5.2870935 -38.4167849 48.990972 -61.552221 72.126408
## 2005.1205 4.3670994 -39.3905334 48.124732 -62.554425 71.288624
## 2005.1233 3.8979611 -39.9133602 47.709282 -63.105673 70.901595
## 2005.1260 3.5132505 -40.3516936 47.378195 -63.572392 70.598893
## 2005.1288 4.0474341 -39.8710672 47.965936 -63.120118 71.214986
## 2005.1315 4.7928847 -39.1791088 48.764878 -62.456476 72.042245
## 2005.1342 4.2468832 -39.7785373 48.272304 -63.084187 71.577954
## 2005.1370 0.9770956 -43.1016872 45.055879 -66.435585 68.389777
## 2005.1397 2.8484039 -41.2836768 46.980485 -64.645789 70.342597
## 2005.1425 3.3846878 -40.8006264 47.570002 -64.190919 70.960294
## 2005.1452 3.6441420 -40.5943416 47.882626 -64.012780 71.301064
## 2005.1479 4.8681392 -39.4234500 49.159728 -62.870001 72.606280
## 2005.1507 4.3069849 -40.0376464 48.651616 -63.512276 72.126246
## 2005.1534 3.7691741 -40.6284358 48.166784 -64.131111 71.669459
## 2005.1562 2.5930154 -41.8575101 47.043541 -65.388197 70.574228
## 2005.1589 2.4611128 -42.0422652 46.964491 -65.600930 70.523156
## 2005.1616 4.5474117 -40.0087563 49.103580 -63.595367 72.690190
## 2005.1644 2.7180617 -41.8908337 47.326957 -65.505356 70.941480
## 2005.1671 4.5195432 -40.1420173 49.181104 -63.784419 72.823506
## 2005.1699 5.7783941 -38.9357696 50.492558 -62.606018 74.162806
## 2005.1726 5.4957186 -39.2709865 50.262424 -62.969049 73.960486
## 2005.1753 5.1143727 -39.7048121 49.933557 -63.430655 73.659401
## 2005.1781 5.4635696 -39.4080335 50.335173 -63.161625 74.088765
## 2005.1808 2.3467987 -42.5771617 47.270759 -66.358470 71.052067
## 2005.1836 2.0917731 -42.8844835 47.068030 -66.693476 70.877022
## 2005.1863 1.1602201 -43.8682721 46.188712 -67.704916 70.025356
## 2005.1890 4.5096232 -40.5710440 49.590290 -64.435308 73.454554
## 2005.1918 5.9831642 -39.1496176 51.115946 -63.041469 75.007798
## 2005.1945 6.3254152 -38.8594212 51.510252 -62.778829 75.429659
## 2005.1973 4.7334749 -40.5033561 49.970306 -64.450288 73.917238
## 2005.2000 4.0451410 -41.2436250 49.333907 -65.218050 73.308332
## 2005.2027 4.9730091 -40.3676324 50.313651 -64.369518 74.315536
## 2005.2055 6.5103089 -38.8821489 51.902767 -62.911464 75.932082
## 2005.2082 6.2915953 -39.1526196 51.735810 -63.209334 75.792524
## 2005.2110 3.5892818 -41.9066313 49.085195 -65.990713 73.169277
## 2005.2137 4.9373643 -40.6101883 50.484917 -64.721606 74.596335
## 2005.2164 5.7682546 -39.8308791 51.367388 -63.969602 75.506112
## 2005.2192 5.9599906 -39.6906659 51.610647 -63.856664 75.776645
## 2005.2219 3.9184128 -41.7837085 49.620534 -65.976950 73.813776
## 2005.2247 5.4870188 -40.2665092 51.240547 -64.486964 75.461002
## 2005.2274 6.5354177 -39.2694596 52.340295 -63.517097 76.587932
## 2005.2301 6.4289092 -39.4272597 52.285078 -63.702049 76.559868
## 2005.2329 8.0451317 -37.8622715 53.952535 -62.164183 78.254446
## 2005.2356 8.5012418 -37.4573386 54.459822 -61.786341 78.788825
## 2005.2384 9.4622148 -36.5474859 55.471915 -60.903550 79.827980
## 2005.2411 8.8449054 -37.2158588 54.905670 -61.598955 79.288765
## 2005.2438 6.7650464 -39.3467249 52.876818 -63.756822 77.286915
## 2005.2466 7.4315769 -38.7311450 53.594299 -63.168214 78.031368
## 2005.2493 7.3183509 -38.8952654 53.531967 -63.359276 77.995978
## 2005.2521 8.8912614 -37.3731935 55.155716 -61.864116 79.646639
## 2005.2548 8.7565501 -37.5586874 55.071788 -62.076493 79.589593
## 2005.2575 8.4205126 -37.9454520 54.786477 -62.490111 79.331136
## 2005.2603 7.1952933 -39.2213429 53.611929 -63.792826 78.183412
## 2005.2630 8.8721698 -37.5950828 55.339422 -62.193360 79.937700
## 2005.2658 9.8584377 -36.6593761 56.376252 -61.284419 81.001295
## 2005.2685 10.2399790 -36.3283413 56.808299 -60.980121 81.460079
## 2005.2712 8.9237045 -37.6950675 55.542476 -62.373555 80.220964
## 2005.2740 8.5458797 -38.1232894 55.215049 -62.828455 79.920215
## 2005.2767 6.9993236 -39.7201882 53.718835 -64.452004 78.450651
## 2005.2795 6.3824239 -40.3873765 53.152224 -65.145813 77.910661
## 2005.2822 7.4904390 -39.3295959 54.310474 -64.114625 79.095503
## 2005.2849 8.5990955 -38.2711202 55.469311 -63.082714 80.280905
## 2005.2877 8.4638796 -38.4564631 55.384222 -63.294592 80.222351
## 2005.2904 9.8294611 -37.1409552 56.799877 -62.005592 81.664514
## 2005.2932 10.2541953 -36.7662413 57.274632 -61.657357 82.165747
## 2005.2959 9.8972717 -37.1731319 56.967675 -62.090698 81.885242
## 2005.2986 8.9201787 -38.2001390 56.040496 -63.144128 80.984486
## 2005.3014 7.8102626 -39.3599164 54.980442 -64.330301 79.950826
## 2005.3041 6.8926315 -40.3273562 54.112619 -65.324108 79.109371
## 2005.3068 7.6653450 -39.6043988 54.935089 -64.627490 79.958180
## 2005.3096 8.1789631 -39.1404845 55.498411 -64.189887 80.547813
## 2005.3123 9.2212045 -38.1478948 56.590304 -63.223581 81.665990
## 2005.3151 9.0340546 -38.3846444 56.452754 -63.486587 81.554697
## 2005.3178 9.0605773 -38.4076696 56.528824 -63.535842 81.656996
## 2005.3205 8.7228710 -38.7948721 56.240614 -63.949246 81.394988
## 2005.3233 9.5554062 -38.0117815 57.122594 -63.192330 82.303142
## 2005.3260 9.1572267 -38.4593543 56.773808 -63.666050 81.980503
## 2005.3288 7.5535666 -40.1123566 55.219490 -65.345172 80.452305
## 2005.3315 6.9332012 -40.7820131 54.648416 -66.040922 79.907324
## 2005.3342 7.1178009 -40.6466538 54.882256 -65.931629 80.167230
## 2005.3370 8.7953890 -39.0182552 56.609033 -64.329270 81.920047
## 2005.3397 9.0849602 -38.7778230 56.947743 -64.114850 82.284770
## 2005.3425 8.7332752 -39.1785967 56.645147 -64.541610 82.008160
## 2005.3452 9.2313540 -38.7295562 57.192264 -64.118528 82.581236
## 2005.3479 9.0852825 -38.9246159 57.095181 -64.339521 82.510086
## 2005.3507 9.3764745 -38.6823624 57.435311 -64.123174 82.876123
## 2005.3534 9.5793047 -38.5284207 57.687030 -63.995112 83.153722
## 2005.3562 8.8195702 -39.3369941 56.976134 -64.829539 82.468680
## 2005.3589 10.1059410 -38.0994127 58.311295 -63.617786 83.829668
## 2005.3616 9.6015698 -38.6525240 57.855664 -64.196698 83.399838
## 2005.3644 9.0110857 -39.2916991 57.313871 -64.861649 82.883820
## 2005.3671 8.5061213 -39.8453054 56.857548 -65.441005 82.453247
## 2005.3699 8.9143140 -39.4857058 57.314334 -65.107129 82.935756
## 2005.3726 9.6320787 -38.8164853 58.080643 -64.463606 83.727763
## 2005.3753 9.8683409 -38.6287188 58.365401 -64.301511 84.038193
## 2005.3781 8.8422073 -39.7032997 57.387714 -65.401739 83.086153
## 2005.3808 9.6363068 -38.9575991 58.230213 -64.681659 83.954273
## 2005.3836 10.0362880 -38.6059687 58.678545 -64.355624 84.428200
## 2005.3863 9.9514910 -38.7390684 58.642050 -64.514294 84.417276
## 2005.3890 9.6098406 -39.1289738 58.348655 -64.929744 84.149425
## 2005.3918 8.3577870 -40.4292345 57.144809 -66.255524 82.971098
## 2005.3945 8.4181658 -40.4170153 57.253347 -66.268799 83.105130
## 2005.3973 8.8443519 -40.0389414 57.727645 -65.916194 83.604897
## 2005.4000 9.2091634 -39.7221947 58.140521 -65.624891 84.043218
## 2005.4027 9.8409131 -39.1384626 58.820289 -65.066578 84.748404
## 2005.4055 9.6744978 -39.3528486 58.701844 -65.306358 84.655354
## 2005.4082 9.6301029 -39.4451673 58.705373 -65.424046 84.684252
## 2005.4110 10.9915218 -38.1316253 60.114669 -64.135849 86.118892
## 2005.4137 10.4781057 -38.6928718 59.649083 -64.722415 85.678626
## 2005.4164 10.2786718 -38.9400896 59.497433 -64.994928 85.552272
## 2005.4192 10.2211904 -39.0453085 59.487689 -65.125418 85.567798
## 2005.4219 9.5005260 -39.8136643 58.814716 -65.919020 84.920072
## 2005.4247 9.6324162 -39.7294193 58.994252 -65.859997 85.124829
## 2005.4274 9.4938697 -39.9155652 58.903305 -66.071340 85.059079
## 2005.4301 8.6067546 -40.8502338 58.063743 -67.031182 84.244691
## 2005.4329 8.8864575 -40.6180386 58.390954 -66.824136 84.597051
## 2005.4356 9.0560002 -40.4959582 58.607959 -66.727181 84.839181
## 2005.4384 9.3078080 -40.2915673 58.907183 -66.547891 85.163507
## 2005.4411 8.3679678 -41.2787791 58.014715 -67.560179 84.296115
## 2005.4438 9.3940601 -40.3000132 59.088133 -66.606467 85.394587
## 2005.4466 9.1995329 -40.5418218 58.940888 -66.873304 85.272370
## 2005.4493 8.9756158 -40.8129753 58.764207 -67.169463 85.120695
## 2005.4521 8.6017445 -41.2340384 58.437527 -67.615508 84.818997
## 2005.4548 8.6920610 -41.1908690 58.574991 -67.597297 84.981419
## 2005.4575 8.8703828 -41.0596497 58.800415 -67.491012 85.231778
## 2005.4603 8.5144784 -41.4626123 58.491569 -67.918886 84.947843
## 2005.4630 9.1506087 -40.8734959 59.174713 -67.354657 85.655875
## 2005.4658 9.0227440 -41.0483303 59.093818 -67.554356 85.599844
## 2005.4685 9.1610218 -40.9569782 59.279022 -67.487845 85.809888
## 2005.4712 9.9443191 -40.2205628 60.109201 -66.776247 86.664885
## 2005.4740 10.1849243 -40.0267956 60.396644 -66.607274 86.977123
## 2005.4767 9.8216771 -40.4368372 60.080191 -67.042088 86.685442
## 2005.4795 10.2126839 -40.0925812 60.517949 -66.722580 87.147948
## 2005.4822 10.2317930 -40.1201796 60.583766 -66.774904 87.238490
## 2005.4849 9.8872820 -40.5113548 60.285919 -67.190782 86.965346
## 2005.4877 10.2421564 -40.2031015 60.687414 -66.907208 87.391521
## 2005.4904 10.2527978 -40.2390380 60.744634 -66.967801 87.473397
## 2005.4932 10.1538837 -40.3844871 60.692255 -67.137885 87.445652
## 2005.4959 10.2407475 -40.3441156 60.825611 -67.122125 87.603620
## 2005.4986 10.1650815 -40.4662311 60.796394 -67.268829 87.598992
## 2005.5014 10.1277208 -40.5499988 60.805440 -67.377163 87.632605
## 2005.5041 10.0705527 -40.6535314 60.794637 -67.505240 87.646345
## 2005.5068 10.5337643 -40.2366419 61.304171 -67.112872 88.180400
## 2005.5096 10.1784045 -40.6382817 60.995091 -67.539010 87.895819
## 2005.5123 10.2580593 -40.6048648 61.120983 -67.530070 88.046189
## 2005.5151 10.1565566 -40.7525632 61.065677 -67.702223 88.015337
## 2005.5178 10.1087691 -40.8465047 61.064043 -67.820597 88.038136
## 2005.5205 10.0362993 -40.9650867 61.037685 -67.963590 88.036188
## 2005.5233 9.6718450 -41.3756115 60.719302 -68.398503 87.742193
## 2005.5260 9.4063739 -41.6871117 60.499859 -68.734369 87.547117
## 2005.5288 9.3140676 -41.8254055 60.453541 -68.897007 87.525143
## 2005.5315 10.0602552 -41.1251642 61.245675 -68.221088 88.341599
## 2005.5342 10.6482731 -40.5830513 61.879597 -67.703276 88.999822
## 2005.5370 10.2382235 -41.0389649 61.515412 -68.183469 88.659916
## 2005.5397 9.9298008 -41.3932105 61.252812 -68.561972 88.421573
## 2005.5425 10.5654203 -40.8033731 61.934214 -67.996370 89.127210
## 2005.5452 10.7652659 -40.6492688 62.179801 -67.866479 89.397011
## 2005.5479 9.7845167 -41.6757186 61.244752 -68.917122 88.486155
## 2005.5507 9.0395213 -42.4663742 60.545417 -69.731948 87.810991
## 2005.5534 8.5537031 -42.9978120 60.105218 -70.287536 87.394942
## 2005.5562 8.9853516 -42.6117429 60.582446 -69.925595 87.896298
## 2005.5589 9.8705768 -41.7720568 61.513210 -69.110016 88.851169
## 2005.5616 9.6709696 -42.0171630 61.359102 -69.379208 88.721147
## 2005.5644 10.1361772 -41.5974143 61.869769 -68.983523 89.255878
## 2005.5671 10.2615480 -41.5174626 62.040559 -68.927615 89.450711
## 2005.5699 10.2924728 -41.5319170 62.116863 -68.966092 89.551037
## 2005.5726 10.2770604 -41.5926690 62.146790 -69.050845 89.604966
## 2005.5753 9.9876609 -41.9273684 61.902690 -69.409525 89.384847
## 2005.5781 10.4778448 -41.4824450 62.438135 -68.988561 89.944251
## 2005.5808 10.1663966 -41.8391143 62.171907 -69.369169 89.701962
## 2005.5836 10.5867371 -41.4639555 62.637430 -69.017928 90.191402
## 2005.5863 9.8003730 -42.2954623 61.896208 -69.873332 89.474078
## 2005.5890 10.1985698 -41.9423690 62.339509 -69.544115 89.941254
## 2005.5918 10.3443720 -41.8416313 62.530375 -69.467233 90.155977
## 2005.5945 10.4943412 -41.7366877 62.725370 -69.386124 90.374807
## 2005.5973 9.6246529 -42.6513629 61.900669 -70.324614 89.573920
## 2005.6000 9.7902271 -42.5307370 62.111191 -70.227782 89.808236
## 2005.6027 9.8565647 -42.5093089 62.222438 -70.230128 89.943257
## 2005.6055 9.9126685 -42.4980763 62.323413 -70.242649 90.067986
## 2005.6082 9.4206484 -43.0349291 61.876226 -70.803234 89.644531
## 2005.6110 10.2728857 -42.2274863 62.773258 -70.019504 90.565276
## 2005.6137 10.5400599 -42.0050683 63.085188 -69.820779 90.900899
## 2005.6164 10.2966706 -42.2931758 62.886517 -70.132559 90.725900
## 2005.6192 9.8083697 -42.8261569 62.442896 -70.689192 90.305932
## 2005.6219 9.5256661 -43.1535028 62.204835 -71.040170 90.091502
## 2005.6247 9.5814856 -43.1422878 62.305259 -71.052568 90.215539
## 2005.6274 9.6249647 -43.1433754 62.393305 -71.077247 90.327177
## 2005.6301 9.2277738 -43.5850956 62.040643 -71.542540 89.998087
## 2005.6329 9.6776200 -43.1797410 62.534981 -71.160738 90.515978
## 2005.6356 9.5081386 -43.3936766 62.409954 -71.398206 90.414483
## 2005.6384 9.6903988 -43.2558333 62.636631 -71.283876 90.664673
## 2005.6411 9.8481057 -43.1425062 62.838718 -71.194042 90.890253
## 2005.6438 9.8367696 -43.1981848 62.871724 -71.273194 90.946733
## 2005.6466 9.8976129 -43.1816471 62.976873 -71.280110 91.075336
## 2005.6493 9.4477551 -43.6757734 62.571284 -71.797671 90.693181
## 2005.6521 10.1127912 -43.0549690 63.280551 -71.200281 91.425864
## 2005.6548 10.5555863 -42.6563689 63.767541 -70.825076 91.936249
## 2005.6575 9.7489903 -43.5071232 63.005104 -71.699207 91.197187
## 2005.6603 9.9416990 -43.3585361 63.241934 -71.573976 91.457374
## 2005.6630 10.1479831 -43.1963372 63.492303 -71.435115 91.731081
## 2005.6658 9.5498076 -43.8385614 62.938177 -72.100657 91.200272
## 2005.6685 9.4137231 -44.0186584 62.846105 -72.304053 91.131499
## 2005.6712 9.6068129 -43.8695449 63.083171 -72.178219 91.391844
## 2005.6740 9.0548033 -44.4654946 62.575101 -72.797429 90.907035
## 2005.6767 9.5596205 -44.0045815 63.123822 -72.359757 91.478998
## 2005.6795 9.2925485 -44.3155216 62.900619 -72.693920 91.279017
## 2005.6822 9.4992808 -44.1526215 63.151183 -72.554223 91.552785
## 2005.6849 9.6608947 -44.0348040 63.356593 -72.459590 91.781379
## 2005.6877 9.2189491 -44.5205104 62.958409 -72.968462 91.406360
## 2005.6904 8.6059664 -45.1772183 62.389151 -73.648316 90.860249
## 2005.6932 9.7487220 -44.0781524 63.575596 -72.572378 92.069822
## 2005.6959 10.2562615 -43.6142670 64.126790 -72.131602 92.644125
## 2005.6986 10.5491299 -43.3650175 64.463277 -71.905443 93.003703
## 2005.7014 9.5014427 -44.4562883 63.459174 -73.019786 92.022671
## 2005.7041 9.7801473 -44.2211321 63.781427 -72.807683 92.367977
## 2005.7068 8.3193953 -45.7253975 62.364188 -74.334983 90.973773
## 2005.7096 7.4988943 -46.5893768 61.587165 -75.221978 90.219767
## 2005.7123 8.1464772 -45.9852373 62.278192 -74.640836 90.933790
## 2005.7151 9.1944363 -44.9806867 63.369559 -73.659265 92.048137
## 2005.7178 10.1383454 -44.0801515 64.356842 -72.781690 93.058381
## 2005.7205 10.4320637 -43.8297723 64.693900 -72.554253 93.418381
## 2005.7233 9.4879223 -44.8172183 63.793063 -73.564623 92.540468
## 2005.7260 8.7143604 -45.6340502 63.062771 -74.404361 91.833082
## 2005.7288 8.4976575 -45.8939888 62.889304 -74.687187 91.682502
## 2005.7315 7.8734705 -46.5613771 62.308318 -75.377445 91.124386
## 2005.7342 7.4479661 -47.0300484 61.925981 -75.868967 90.764900
## 2005.7370 7.7672379 -46.7539096 62.288385 -75.615662 91.150137
## 2005.7397 7.8308069 -46.7334392 62.395053 -75.618006 91.279620
## 2005.7425 6.6069307 -48.0003802 61.214242 -76.907744 90.121606
## 2005.7452 7.2208239 -47.4295179 61.871166 -76.359661 90.801309
## 2005.7479 8.4275325 -46.2658062 63.120871 -75.218711 92.073776
## 2005.7507 7.7589612 -46.9773406 62.495263 -75.952989 91.470911
## 2005.7534 8.1306220 -46.6486093 62.909853 -75.646983 91.908227
## 2005.7562 8.3014454 -46.5206818 63.123573 -75.541763 92.144654
## 2005.7589 6.5187261 -48.3462634 61.383716 -77.390034 90.427487
## 2005.7616 6.7839993 -48.1238191 61.691818 -77.190262 90.758261
## 2005.7644 7.3716476 -47.5789663 62.322261 -76.668064 91.411359
## 2005.7671 6.5046950 -48.4886811 61.498071 -77.600416 90.609806
## 2005.7699 7.7056608 -47.3304442 62.741766 -76.464798 91.876120
## 2005.7726 8.6912089 -46.3875919 63.770010 -75.544548 92.926966
## 2005.7753 8.6051797 -46.5162838 63.726643 -75.695824 92.906184
## 2005.7781 8.8776953 -46.2863980 64.041789 -75.488505 93.243896
## 2005.7808 8.3342666 -46.8724235 63.540957 -76.097080 92.765613
## 2005.7836 8.1834835 -47.0657706 63.432738 -76.312959 92.679926
## 2005.7863 7.1667784 -48.1250069 62.458564 -77.394710 91.728267
## 2005.7890 7.3760709 -47.9582130 62.710355 -77.250413 92.002555
## 2005.7918 7.4626871 -47.9140627 62.839437 -77.228743 92.154117
## 2005.7945 7.6513501 -47.7678331 63.070533 -77.104977 92.407677
## 2005.7973 6.8843199 -48.5772641 62.345904 -77.936853 91.705493
## 2005.8000 6.3360318 -49.1679208 61.839984 -78.549938 91.222002
## 2005.8027 7.6684639 -47.8778248 63.214753 -77.282254 92.619182
## 2005.8055 7.2126868 -48.3759059 62.801280 -77.802729 92.228103
## 2005.8082 6.7247170 -48.9061475 62.355582 -78.355348 91.804782
## 2005.8110 5.9564544 -49.7166498 61.629559 -79.188211 91.101120
## 2005.8137 6.8514132 -48.8638987 62.566725 -78.357803 92.060630
## 2005.8164 5.2032611 -50.5542264 60.960749 -80.070457 90.476980
## 2005.8192 4.5483747 -51.2512567 60.348006 -80.789797 89.886547
## 2005.8219 4.7023620 -51.1393814 60.544105 -80.700215 90.104939
## 2005.8247 6.1656495 -49.7181742 62.049473 -79.301283 91.632583
## 2005.8274 5.6057306 -50.3201417 61.531603 -79.925510 91.136971
## 2005.8301 5.0979558 -50.8699336 61.065845 -80.497545 90.693456
## 2005.8329 5.2180558 -50.7918191 61.227931 -80.441656 90.877767
## 2005.8356 4.4430907 -51.6087383 60.494920 -81.280784 90.166966
## 2005.8384 5.5972037 -50.4965480 61.690955 -80.190786 91.385194
## 2005.8411 5.4255543 -50.7100888 61.561197 -80.426503 91.277612
## 2005.8438 4.9948131 -51.1826901 61.172316 -80.921264 90.910890
## 2005.8466 4.7252441 -51.4940881 60.944576 -81.254805 90.705293
## 2005.8493 4.3867674 -51.8743626 60.647898 -81.657206 90.430741
## 2005.8521 4.5224429 -51.7804541 60.825340 -81.585407 90.630293
## 2005.8548 4.9704096 -51.3742232 61.315042 -81.201270 91.142089
## 2005.8575 4.2412825 -52.1450553 60.627620 -81.994179 90.476744
## 2005.8603 4.9185991 -51.5094128 61.346611 -81.380598 91.217796
## 2005.8630 4.8126553 -51.6570001 61.282311 -81.550230 91.175541
## 2005.8658 5.8985388 -50.6127293 62.409807 -80.527988 92.325065
## 2005.8685 3.4815656 -53.0712846 60.034416 -83.008555 89.971686
## 2005.8712 4.2936370 -52.3007648 60.888039 -82.260031 90.847305
## 2005.8740 5.1536441 -51.4822788 61.789567 -81.463525 91.770813
## 2005.8767 5.0986342 -51.5787794 61.776048 -81.581990 91.779258
## 2005.8795 3.4980516 -53.2208223 60.216925 -83.245980 90.242084
## 2005.8822 4.3913361 -52.3689677 61.151640 -82.416058 91.198730
## 2005.8849 4.8789595 -51.9227442 61.680663 -81.991750 91.749669
## 2005.8877 4.1923813 -52.6506920 61.035455 -82.741597 91.126360
## 2005.8904 2.1794616 -54.7049513 59.063874 -84.817741 89.176664
## 2005.8932 3.8463571 -53.0793653 60.772080 -83.214022 90.906737
## 2005.8959 4.2514796 -52.7155224 61.218482 -82.872032 91.374991
## 2005.8986 3.6108375 -53.3974142 60.619089 -83.575760 90.797435
## 2005.9014 6.3421416 -50.7073300 63.391613 -80.907496 93.591779
## 2005.9041 4.9167190 -52.1739427 62.007381 -82.395913 92.229351
## 2005.9068 4.4882731 -52.6435490 61.620095 -82.887309 91.863855
## 2005.9096 4.8616170 -52.3113359 62.034570 -82.576869 92.300103
## 2005.9123 5.2652872 -51.9487669 62.479341 -82.236058 92.766632
## 2005.9151 3.2647330 -53.9903929 60.519859 -84.299426 90.828892
## 2005.9178 4.1288065 -53.1673616 61.424975 -83.498121 91.755734
## 2005.9205 5.0326986 -52.3044823 62.369880 -82.656952 92.722350
## 2005.9233 2.9132172 -54.4649474 60.291382 -84.839113 90.665547
## 2005.9260 3.5113647 -53.9077542 60.930484 -84.303600 91.326329
## 2005.9288 4.4125137 -53.0475303 61.872558 -83.465040 92.290068
## 2005.9315 2.3753115 -55.1256285 59.876251 -85.564787 90.315410
## 2005.9342 3.8301764 -53.7116305 61.371983 -84.172423 91.832776
## 2005.9370 2.9886507 -54.5939942 60.571296 -85.076405 91.053706
## 2005.9397 1.4142790 -56.2091749 59.037733 -86.713189 89.541747
## 2005.9425 2.8681940 -54.7960400 60.532428 -85.321642 91.058030
## 2005.9452 3.6526821 -54.0523032 61.357667 -84.599477 91.904841
## 2005.9479 3.3844785 -54.3612293 61.130186 -84.929960 91.698918
## 2005.9507 1.6235840 -56.1628177 59.409986 -86.753091 90.000259
## 2005.9534 2.4069517 -55.4201152 60.234019 -86.031915 90.845819
## 2005.9562 0.8795863 -56.9881172 58.747290 -87.621429 89.380602
## 2005.9589 3.3722012 -54.5361104 61.280513 -85.190919 91.935321
## 2005.9616 2.5871211 -55.3617701 60.536012 -86.038060 91.212302
## 2005.9644 1.6026269 -56.3868155 59.592069 -87.084572 90.289826
## 2005.9671 1.2869734 -56.7429920 59.316939 -87.462200 90.036147
## 2005.9699 1.9267866 -56.1436735 59.997247 -86.884318 90.737891
## 2005.9726 0.1962828 -57.9146437 58.307209 -88.676710 89.069276
## 2005.9753 1.5884800 -56.5628847 59.739845 -87.346358 90.523318
## 2005.9781 3.2312324 -54.9605425 61.423007 -85.765407 92.227872
## 2005.9808 2.3686729 -55.8634841 60.600830 -86.689726 91.427072
## 2005.9836 2.0739974 -56.1985137 60.346509 -87.046118 91.194113
## 2005.9863 1.0336628 -57.2791745 59.346500 -88.148126 90.215452
## 2005.9890 -0.2355325 -58.5886682 58.117603 -89.478952 89.007887
## 2005.9918 1.7310214 -56.6623848 60.124428 -87.573987 91.036030
## 2005.9945 1.5290033 -56.9046456 59.962652 -87.837551 90.895558
## 2005.9973 1.2229817 -57.2508823 59.696846 -88.205076 90.651040
## 2006.0000 3.5028204 -55.0112311 62.016872 -85.986699 92.992340
## 2006.0027 2.5034075 -56.0508038 61.057619 -87.047531 92.054346
## 2006.0055 2.4826142 -56.1117294 61.076958 -87.129701 92.094930##NOTE: AIC = 19695.46 , BIC = 19712.54 , RMSE = 1.901511
Also, the headline of the plot below contains ETS(A,N,N) showing that the automated model characterized error of the “tsWSR_PK” SERIES as Additative (A), trend as None (A) and seasonality as None (N) which is equivalent to simple exponential model(ses) with only alpha parameter i.e level.
#Model 2 : ARIMA Model
It is used for forecasting for both seasonal and non- seasonal level.
#Changing to stationary set
train.sta_Var7 <- diff(train6)
test.sta_Var7 <- diff(test6)#2.1 Auto Arima model without sesonality:
set.seed(301)
model_Var7 <- auto.arima(train.sta_Var7, seasonal = FALSE)
summary(model_Var7)## Series: train.sta_Var7
## ARIMA(1,0,2) with zero mean
##
## Coefficients:
## ar1 ma1 ma2
## 0.5610 -0.7735 -0.1367
## s.e. 0.0359 0.0392 0.0303
##
## sigma^2 estimated as 4.081: log likelihood=-4650.53
## AIC=9309.05 AICc=9309.07 BIC=9331.82
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 0.005417012 2.018759 1.438273 NaN Inf 0.6448721 0.001386656##AIC = 9309.05 , BIC = 9331.82, RMSE = 2.018759
tsdisplay(residuals(model_Var7), lag.max = 45, main = '(1,1,1) Model Residuals')
#2.2 Auto Arima model with sesonality:
set.seed(301)
model2_Var7 <- auto.arima(train.sta_Var7, seasonal= TRUE)
summary(model2_Var7)## Series: train.sta_Var7
## ARIMA(4,0,1) with zero mean
##
## Coefficients:
## ar1 ar2 ar3 ar4 ma1
## 0.7052 -0.0995 -0.0066 0.0020 -0.9163
## s.e. 0.0273 0.0264 0.0264 0.0238 0.0170
##
## sigma^2 estimated as 4.083: log likelihood=-4650.13
## AIC=9312.26 AICc=9312.3 BIC=9346.42
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 0.005187141 2.018396 1.437818 NaN Inf 0.6446682 -3.497019e-05##AIC = 9312.26 , BIC = 9346.42, RMSE = 2.018396
tsdisplay(residuals(model2_Var7), lag.max = 40, main = 'Seasonal Model Residuals')
NOTE: Above Graphs does not shows serious lags.
Fit the observed with the predicted values for both models in the same plot.
par(mfrow = c(2,2))
fit_auto_train_Var7 %>% forecast(h=341) %>% autoplot() 
model2_Var7 %>% forecast(h=341) %>% autoplot() 
model_Var7 %>% forecast(h=341) %>% autoplot() 
Plot and comment on the residuals of the fitted data for both models in the same plot.
Residual Plot - to confirm no problem with this model
par(mfrow= c(3,2))
hist(fit_auto_train_Var7$residuals,col = 'red',xlab = 'Error',main = 'Histogram Of Residuals',freq= FALSE)
lines(density(fit_auto_train_Var7$residuals))
hist(model_Var7$residuals,col = 'red',xlab = 'Error',main = 'Histogram Of Residuals',freq= FALSE)
lines(density(model_Var7$residuals))
hist(model2_Var7$residuals,col = 'red',xlab = 'Error',main = 'Histogram Of Residuals',freq= FALSE)
lines(density(model2_Var7$residuals))
OBSERVATION: The residuals for each model are normally distributed, which shows the good fit of the models. It is normally distrbuted.
Testing the autocorrelation and partial autocorrelation of the residuals (using the plots and Ljung-Box Q statistic) up to an appropriate lag *
#ACF PLOTS & PACF PLOTS
par(mfrow = c(3,2))
acf(fit_auto_train_Var7$residuals, main = 'Correlogram')
pacf(fit_auto_train_Var7$residuals, main = 'Partial Corelogram')
acf(model_Var7$residuals, main = 'Correlogram')
pacf(model_Var7$residuals, main = 'Partial Corelogram')
acf(model2_Var7$residuals, main = 'Correlogram')
pacf(model2_Var7$residuals, main = 'Partial Corelogram')
NOTE:
1. Residuals are the difference between actaual and fitted values
2. These blue lines are signficance bounds
3. This graph shows us the autocorelations for insample forecast errors
. 4. Do not exceed these significance bounds for lags 1 to end
- Ljunx-Box Test to check the autocorelations of the residuals
HO: No serial correlation upto 20 lags (does not exhibit lack of fit of the model)
Ha: Serial corelation is present (the model exhibits lack of fit)
We reject the null hypothesis, if p value is less than 0.05. This test is generally done for ARIMA models
Box.test(model_Var7$residuals, lag =20, type = 'Ljung-Box')##
## Box-Ljung test
##
## data: model_Var7$residuals
## X-squared = 33.203, df = 20, p-value = 0.03205Box.test(model2_Var7$residuals, lag =20, type = 'Ljung-Box')##
## Box-Ljung test
##
## data: model2_Var7$residuals
## X-squared = 31.847, df = 20, p-value = 0.04496OBSERVATIONS:
For above performed Ljunx-Box Test on models, there is little statistical significance. We conclude that there is a liitle evidence of non-zero auto-corelations in the insample forecast errors at lags 1 to 20.
Test and comment on the normality of the residuals.
Here, further testing the normality by plotting Normal Q-Q plots. From below plots we observed that most of the datapoints lies on the line. Hence, we could conclude that our model produces residuals that are normal
par(mfrow = c(2,2))
qqnorm(fit_auto_train_Var7$residuals)
qqnorm(model_Var7$residuals)
qqnorm(model2_Var7$residuals)
Validating The Model by testing the model performance with Holdout set
Here, choosing RMSE as evaluation parameter. The lower RMSE indicates a more accurate forecast.
Below, is the comparison of model. We are fitting the model to test set which is the holdout set. And checking the accuracy using RMSE(Root mean square error) evaluation parameter.
accuracy(forecast(fit_auto_train_Var7), test6) ["Test set", "RMSE"]## [1] 2.870951#o/p - 2.870951
accuracy(forecast(model2_Var7), test.sta_Var7) ["Test set", "RMSE"]## [1] 2.00263#o/p -2.00263
accuracy(forecast(model_Var7), test.sta_Var7) ["Test set", "RMSE"]## [1] 2.002481#O/P - 2.002481
NOTE:- Here, the RMSE value is less of ARIMA models compared to exponential model.
The minimum RMSE is of model_Var7
COMMENT ON BEST MODEL AND ITS PARAMETERS
We observed the best model to be ARIMA model i.e.“model_Var7”.
summary(model_Var7)## Series: train.sta_Var7
## ARIMA(1,0,2) with zero mean
##
## Coefficients:
## ar1 ma1 ma2
## 0.5610 -0.7735 -0.1367
## s.e. 0.0359 0.0392 0.0303
##
## sigma^2 estimated as 4.081: log likelihood=-4650.53
## AIC=9309.05 AICc=9309.07 BIC=9331.82
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 0.005417012 2.018759 1.438273 NaN Inf 0.6448721 0.001386656Passing parameter order = (1,0,2) ,which means
p = 1, d = 0 q = 2
For the best model, 1 member of lag is used as a predictor. As we transformed the series to stationary so members of differences needed for stationarity is 0. 2 are the number of lagged forecasts errors used in the prediction equation. AIC = 9309.07, RMSE = 2.018759 which is minimum as compared to other models.
8. Forecasting on K-Index (KI)
#Checking the attributes of time series
attributes(tsKI)## $tsp
## [1] 1998.00 2004.94 365.00
##
## $class
## [1] "ts"#Plotting the series
plot(tsKI, main = "Average T observed for years (tsKI)", col = "red")
From the plot, we observes that there is no trend but seems to have seasonlity.
Checking the statistics and visualising the missing data in the series:
plotNA.distribution(tsKI)
Here, data is missing at random.
#Impute the missing values with “na_interpolation” function of “imputeTS package” and visualise the imputed values in the time series
tsKI.imp <- na_interpolation(tsKI, method = "linear")
plotNA.imputations(tsKI, tsKI.imp)
#Decomposition Of Time Series
decomp7 <- decompose(tsKI.imp)
plot(decomp7, col = "red")
OBSERVATIONS:
1)There does seems to have trend.
2)We observes the downward trend from year 1999 to mid of year 2001 and then upward trend from year onwards.
3)We observe some seasonality in the series.Seasonality describes cyclical effects due to the time of the year.
Let’s explore this seasonality pattern by plotting the decomp$seasonal components such that y-axis represents Seasonality Index and x-axis has month
#Plotting the decomposed series
plot(decomp7$seasonal[1:365], type ='b', xlab = 'Years', ylab = 'Seasonality Index', col = 'blue', las = 2, main = "SEASONAL DATA")
OBSERVATIONS:
- There is increase in KI for mid month of the year
- There is a huge drop of KI for starting and end months of the year
#Stationarity check of time series
We could check the stationarity of time series by ADF and KPSS Tests:
- Augmented Dickey- Fuller(ADF) t-statistic test for unit root
- Kwiatkowski-Phillips-Schmidt-Shin (KPSS) for level or trend stationarity
adf.test(tsKI.imp)## Warning in adf.test(tsKI.imp): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: tsKI.imp
## Dickey-Fuller = -5.9654, Lag order = 13, p-value = 0.01
## alternative hypothesis: stationary#p-value is smaller, hence series is stationary
kpss.test(tsKI.imp, null = "Trend")##
## KPSS Test for Trend Stationarity
##
## data: tsKI.imp
## KPSS Trend = 0.12165, Truncation lag parameter = 8, p-value = 0.09509#series is not stationary
acf(tsKI.imp,lag.max = length(tsT70.imp),xlab = "lag #", ylab = 'ACF',main='Statiionary Check ')
Here, we observes most of the data lies outside the blue-dotted lines means the significance level.
Now, we will take the difference to make our data stationary.
It seems difference of 1 is sufficient to make the series stationary.
tsKI.sta <- diff(tsKI.imp)
acf(tsKI.sta, lag.max = length(tsKI.sta),xlab = "lag #", ylab = 'ACF',main='Statiionary Check ')
Hence, after differencing our series is now transformed to stationary time series.
#CREATING MODELS AND FORECASTING: USING EXPONENTIAL SMOOTHING AND ARIMA TECHNIQUES FOR TIME SERIES FORECASTING
#Visualising the stationary series
#plotting the transformed stationary series
plot(tsKI.sta, col = "red")
- TRAIN- TEST SET SPLIT
train7 <- window(tsKI.imp, end = c(2004, 3))
test7 <- window(tsKI.imp, start = c(2004, 4))#Model 1 : Auto Exponential Smoothening Model
set.seed(301)
fit_auto_train_Var8 <- forecast(train7)
summary(fit_auto_train_Var8)##
## Forecast method: STL + ETS(A,N,N)
##
## Model Information:
## ETS(A,N,N)
##
## Call:
## ets(y = na.interp(x), model = etsmodel, allow.multiplicative.trend = allow.multiplicative.trend)
##
## Smoothing parameters:
## alpha = 0.3354
##
## Initial states:
## l = 14.2489
##
## sigma: 14.8835
##
## AIC AICc BIC
## 28718.12 28718.13 28735.20
##
## Error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 0.01592438 14.87674 11.11423 Inf Inf 0.5984462 0.2408974
##
## Forecasts:
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 2004.0082 18.880269119 -0.1937416 37.95428 -10.290913 48.05145
## 2004.0110 28.090116005 7.9719178 48.20831 -2.678013 58.85824
## 2004.0137 27.992483454 6.8816826 49.10328 -4.293700 60.27867
## 2004.0164 31.624741870 9.5659585 53.68353 -2.111256 65.36074
## 2004.0192 9.096112091 -13.8715595 32.06378 -26.029910 44.22213
## 2004.0219 15.296380701 -8.5455561 39.13832 -21.166715 51.75948
## 2004.0247 20.648317134 -4.0369409 45.33358 -17.104527 58.40116
## 2004.0274 8.434968649 -17.0657368 33.93567 -30.564995 47.43493
## 2004.0301 21.361635444 -4.9292373 47.65251 -18.846785 61.57006
## 2004.0329 11.016897487 -16.0410774 38.07487 -30.364704 52.39850
## 2004.0356 13.634269363 -14.1696516 41.43819 -28.888158 56.15670
## 2004.0384 20.632098920 -7.8982714 49.16247 -23.001337 64.26554
## 2004.0411 24.126739699 -5.1120367 53.36552 -20.590110 68.84359
## 2004.0438 30.134130746 0.2037105 60.06455 -15.640497 75.90876
## 2004.0466 11.517810221 -19.0886282 42.12425 -35.290698 58.32632
## 2004.0493 22.387615713 -8.8802286 53.65546 -25.432425 70.20766
## 2004.0521 17.013288253 -14.9022581 48.92883 -31.797328 65.82390
## 2004.0548 6.557020871 -25.9933418 39.10738 -43.224463 56.33850
## 2004.0575 2.741376067 -30.4316571 35.91441 -47.992400 53.47515
## 2004.0603 17.059782153 -16.7244470 50.84401 -34.608738 68.72830
## 2004.0630 10.029250521 -24.3553122 44.41381 -42.557400 62.61590
## 2004.0658 23.029083963 -11.9455092 58.00368 -30.459940 76.51811
## 2004.0685 15.985678246 -19.5691552 51.54051 -38.390747 70.36210
## 2004.0712 1.538199489 -34.5875558 37.66395 -53.711375 56.78777
## 2004.0740 5.807256382 -30.8805373 42.49505 -50.301882 61.91639
## 2004.0767 15.671677248 -21.5696737 52.91303 -41.284054 72.62741
## 2004.0795 23.767774695 -14.0190250 61.55457 -34.022149 81.55770
## 2004.0822 23.278159899 -15.0463264 61.60265 -35.334084 81.89040
## 2004.0849 27.079270172 -11.7754626 65.93400 -32.343916 86.50246
## 2004.0877 17.181044951 -22.1967949 56.55888 -43.042164 77.40425
## 2004.0904 18.056181698 -21.8379067 57.95027 -42.956561 79.06892
## 2004.0932 28.264400931 -12.1393403 68.66814 -33.527789 90.05659
## 2004.0959 11.362886107 -29.5441587 52.26993 -51.199040 73.92481
## 2004.0986 11.615294457 -29.7889364 53.01953 -51.707012 74.93760
## 2004.1014 7.139396851 -34.7561201 49.03491 -56.934267 71.21306
## 2004.1041 9.188190800 -33.1929177 51.56930 -55.628121 74.00450
## 2004.1068 12.833606304 -30.0275926 55.69481 -52.716941 78.38415
## 2004.1096 25.168002869 -18.1679681 68.50397 -41.108645 91.44465
## 2004.1123 14.887916867 -28.9176809 58.69351 -52.106964 81.88280
## 2004.1151 20.562243332 -23.7079996 64.83249 -47.143251 88.26774
## 2004.1178 26.142123528 -18.5879382 70.87219 -42.266603 94.55085
## 2004.1205 20.450762835 -24.7344387 65.63596 -48.654040 89.55557
## 2004.1233 0.216738388 -45.4190639 45.85254 -69.577198 70.01068
## 2004.1260 9.690306711 -36.3916905 55.77230 -60.786026 80.16664
## 2004.1288 16.795142737 -29.7287702 63.31906 -54.357042 87.94733
## 2004.1315 21.157622359 -25.8040481 68.11929 -50.664055 92.97930
## 2004.1342 26.046995187 -21.3483897 73.44238 -46.437991 98.53198
## 2004.1370 11.236546173 -36.5886200 59.06171 -61.905734 84.37883
## 2004.1397 5.522144366 -42.7289751 53.77326 -68.271575 79.31586
## 2004.1425 14.397208105 -34.2761372 63.07055 -60.042250 88.83667
## 2004.1452 21.080217937 -28.0117219 70.17216 -53.999425 96.15986
## 2004.1479 23.120652307 -26.3863429 72.62765 -52.593763 98.83507
## 2004.1507 33.447796921 -16.4708027 83.36640 -42.896113 109.79171
## 2004.1534 18.657029080 -31.6698087 68.98387 -58.311227 95.62529
## 2004.1562 21.856864632 -28.8749263 72.58866 -55.730714 99.44444
## 2004.1589 23.957806403 -27.1757308 75.09134 -54.244190 102.15980
## 2004.1616 3.181118701 -48.3510328 54.71327 -75.630506 81.99274
## 2004.1644 18.756933734 -33.1707723 70.68464 -60.659639 98.17351
## 2004.1671 27.941333934 -24.3789362 80.26160 -52.075614 107.95828
## 2004.1699 15.563827832 -37.1460828 68.27374 -65.049024 96.17668
## 2004.1726 24.900626317 -28.1960656 77.99732 -56.303756 106.10501
## 2004.1753 27.526303523 -25.9543725 81.00698 -54.265332 109.31794
## 2004.1781 20.273941434 -33.5879813 74.13586 -62.100761 102.64864
## 2004.1808 26.248734579 -27.9917552 80.48922 -56.704936 109.20241
## 2004.1836 3.257296699 -51.3591362 57.87373 -80.271329 86.78592
## 2004.1863 12.061090960 -42.9287150 67.05090 -72.038560 96.16074
## 2004.1890 8.170267190 -47.1903937 63.53093 -76.496557 92.83709
## 2004.1918 3.072079221 -52.6569687 58.80113 -82.158145 88.30230
## 2004.1945 11.653018862 -44.4419970 67.74803 -74.136905 97.44294
## 2004.1973 33.228386511 -23.2302250 89.68700 -53.117609 119.57438
## 2004.2000 32.140889334 -24.6789912 88.96077 -54.757619 119.03940
## 2004.2027 30.786462367 -26.3924047 87.96533 -56.661069 118.23399
## 2004.2055 31.110109544 -26.4255043 88.64572 -56.883018 119.10324
## 2004.2082 30.641157178 -27.2490049 88.53132 -57.894206 119.17652
## 2004.2110 25.329533742 -32.9130184 83.57209 -63.744763 114.40383
## 2004.2137 16.523344042 -42.0694789 75.11617 -73.086646 106.13333
## 2004.2164 9.586450044 -49.3545621 68.52746 -80.556049 99.72895
## 2004.2192 19.410752563 -39.8764039 78.69791 -71.261129 110.08263
## 2004.2219 23.876615298 -35.7546763 83.50791 -67.321575 115.07481
## 2004.2247 21.821187669 -38.1522644 81.79464 -69.900292 113.54267
## 2004.2274 18.978814332 -41.3348571 79.29249 -73.262986 111.22061
## 2004.2301 17.711127243 -42.9408552 78.36311 -75.048075 110.47033
## 2004.2329 21.437896663 -39.5505202 82.42631 -71.835838 114.71163
## 2004.2356 15.009968468 -46.3130370 76.33297 -78.775475 108.79541
## 2004.2384 15.524562989 -46.1312155 77.18034 -78.769813 109.81894
## 2004.2411 22.006507138 -39.9802578 83.99327 -72.794069 116.80708
## 2004.2438 35.635903579 -26.6800899 97.95190 -59.668184 130.93999
## 2004.2466 35.555339075 -27.0881527 98.19883 -60.249614 131.36029
## 2004.2493 31.097412158 -31.8718746 94.06670 -65.205801 127.40063
## 2004.2521 25.441565485 -37.8518393 88.73497 -71.357344 122.24047
## 2004.2548 27.923390201 -35.6924812 91.53926 -69.368689 125.21547
## 2004.2575 21.818113088 -42.1185987 85.75482 -75.964649 119.60088
## 2004.2603 21.534438272 -42.7215118 85.79039 -76.736557 119.80543
## 2004.2630 12.810555548 -51.7630547 77.38417 -85.946259 111.56737
## 2004.2658 16.354598160 -48.5351171 81.24431 -82.885657 115.59485
## 2004.2685 19.427540035 -45.7767479 84.63183 -80.293813 119.14889
## 2004.2712 11.308935208 -54.2084150 76.82629 -88.891205 111.50908
## 2004.2740 19.022002118 -46.8069216 84.85093 -81.654649 119.69865
## 2004.2767 22.620740603 -43.5182888 88.75977 -78.530176 123.77166
## 2004.2795 19.332448425 -47.1152394 85.78014 -82.290521 120.95542
## 2004.2822 22.258524969 -44.4963942 89.01344 -79.834314 124.35136
## 2004.2849 20.695403209 -46.3653397 87.75615 -81.865153 123.25596
## 2004.2877 25.110437113 -42.2547413 92.47562 -77.915713 128.13659
## 2004.2904 18.499860579 -49.1683836 86.16810 -84.989788 121.98951
## 2004.2932 27.318672138 -40.6512866 95.28863 -76.632409 131.26975
## 2004.2959 25.171313154 -43.0990267 93.44165 -79.239162 129.58179
## 2004.2986 28.934201197 -39.6352039 97.50361 -75.933654 133.80206
## 2004.3014 34.177254659 -34.6899170 103.04443 -71.145995 139.50050
## 2004.3041 35.553088310 -33.6105679 104.71674 -70.223596 141.32977
## 2004.3068 29.925706452 -39.5331688 99.38458 -76.302476 136.15389
## 2004.3096 29.774574870 -39.9782700 99.52742 -76.903196 136.45235
## 2004.3123 32.551928949 -37.4936518 102.59751 -74.573542 139.67740
## 2004.3151 23.771052765 -46.5660455 94.10815 -83.800256 131.34236
## 2004.3178 28.722123390 -41.9052892 99.34954 -79.293183 136.73743
## 2004.3205 27.549865731 -43.3666727 98.46640 -80.907620 136.00735
## 2004.3233 29.630800512 -41.5736898 100.83529 -79.267070 138.52867
## 2004.3260 32.205083273 -39.2861991 103.69637 -77.131398 141.54156
## 2004.3288 41.492567330 -30.2843611 113.26950 -68.280772 151.26591
## 2004.3315 20.751188140 -51.3102542 92.81263 -89.457278 130.95965
## 2004.3342 16.391298097 -55.9535392 88.73614 -94.250583 127.03318
## 2004.3370 26.704841424 -45.9222851 99.33197 -84.368763 137.77845
## 2004.3397 34.553941744 -38.3543809 107.46226 -76.949716 146.05760
## 2004.3425 28.944217190 -44.2442213 102.13266 -82.987840 140.87627
## 2004.3452 17.901484484 -55.5660018 91.36897 -94.457340 130.26031
## 2004.3479 22.485112991 -51.2603652 96.23059 -90.298863 135.26909
## 2004.3507 27.928351721 -46.0940744 101.95078 -85.279180 141.13588
## 2004.3534 31.728469752 -42.5698720 106.02681 -81.901038 145.35798
## 2004.3562 24.050082740 -50.5231537 98.62332 -89.999841 138.10001
## 2004.3589 17.332488140 -57.5146335 92.17961 -97.136306 131.80128
## 2004.3616 35.988474233 -39.1315339 111.10848 -78.897664 150.87461
## 2004.3644 33.311461768 -42.0804452 108.70337 -81.990510 148.61343
## 2004.3671 36.063841227 -39.5989875 111.72667 -79.652470 151.78015
## 2004.3699 37.097667261 -38.8351166 113.03045 -79.031504 153.22684
## 2004.3726 33.890052530 -42.3117301 110.09184 -82.650517 150.43062
## 2004.3753 33.822035091 -42.6478001 110.29187 -83.128486 150.77256
## 2004.3781 39.122967691 -37.6139837 115.85992 -78.236072 156.48201
## 2004.3808 31.887385312 -45.1157557 108.89053 -85.878756 149.65353
## 2004.3836 29.728702897 -47.5397106 106.99712 -88.443138 147.90054
## 2004.3863 37.576462720 -39.9563158 115.10924 -80.999690 156.15261
## 2004.3890 43.975799615 -33.8204455 121.77204 -75.003290 162.95489
## 2004.3918 42.640092152 -35.4187304 120.69891 -76.740575 162.02076
## 2004.3945 45.603734909 -32.7167847 123.92425 -74.177163 165.38463
## 2004.3973 39.861609121 -38.7197360 118.44295 -80.318187 160.04141
## 2004.4000 43.412981891 -35.4283259 122.25429 -77.164393 163.99036
## 2004.4027 43.252170442 -35.8482457 122.35259 -77.721477 164.22582
## 2004.4055 42.944751885 -36.4139265 122.30343 -78.423873 164.31338
## 2004.4082 41.492540116 -38.1235629 121.10864 -80.269782 163.25486
## 2004.4110 27.178755978 -52.6939419 107.05145 -94.975994 149.33351
## 2004.4137 34.293002690 -45.8354684 114.42147 -88.252919 156.83892
## 2004.4164 38.828027126 -41.5554033 119.21146 -84.107821 161.76388
## 2004.4192 39.497738061 -41.1398457 120.13532 -83.826804 162.82228
## 2004.4219 39.711596473 -41.1793420 120.60253 -84.000418 163.42361
## 2004.4247 41.821443892 -39.3220582 122.96495 -82.276834 165.91972
## 2004.4274 36.044075517 -45.3512066 117.43936 -88.439266 160.52742
## 2004.4301 38.806536470 -42.8397492 120.45282 -86.060682 163.67375
## 2004.4329 40.170682144 -41.7258378 122.06720 -85.079237 165.42060
## 2004.4356 42.061120990 -40.0848709 124.20711 -83.570332 167.69257
## 2004.4384 39.013398331 -43.3813102 121.40811 -86.998434 165.02523
## 2004.4411 38.717526259 -43.9251505 121.36020 -87.673541 165.10859
## 2004.4438 34.694809351 -48.1950937 117.58471 -92.074358 161.46398
## 2004.4466 37.662174380 -45.4742198 120.79857 -89.483968 164.80832
## 2004.4493 42.324875840 -41.0572809 125.70703 -85.197128 169.84688
## 2004.4521 42.198619564 -41.4285774 125.82582 -85.698141 170.09538
## 2004.4548 46.406600309 -37.4649210 130.27812 -81.863822 174.67702
## 2004.4575 44.969034997 -39.1461010 129.08417 -83.673964 173.61203
## 2004.4603 45.215619306 -39.1424278 129.57367 -83.798880 174.23012
## 2004.4630 42.968289598 -41.6319712 127.56855 -86.416644 172.35322
## 2004.4658 45.748242120 -39.0935408 130.59003 -84.006068 175.50255
## 2004.4685 48.471860603 -36.6107589 133.55448 -81.650777 178.59450
## 2004.4712 45.264923321 -40.0578530 130.58770 -85.225002 175.75485
## 2004.4740 40.707023148 -44.8552359 126.26928 -90.149160 171.56321
## 2004.4767 45.016585865 -40.7844875 130.81766 -86.204832 176.23800
## 2004.4795 43.779324149 -42.2599006 129.81855 -87.806315 175.36496
## 2004.4822 42.515374428 -43.7613444 128.79209 -89.433481 174.46423
## 2004.4849 47.167778390 -39.3457826 133.68134 -85.143295 179.47885
## 2004.4877 44.471918307 -42.2778381 131.22167 -88.200385 177.14422
## 2004.4904 41.854779220 -45.1305314 128.84009 -91.177773 174.88733
## 2004.4932 40.830191753 -46.3900368 128.05042 -92.561637 174.22202
## 2004.4959 42.637000372 -44.8175151 130.09152 -91.113139 176.38714
## 2004.4986 45.639852491 -42.0483240 133.32803 -88.467641 179.74735
## 2004.5014 45.747153980 -42.1740625 133.66837 -88.716743 180.21105
## 2004.5041 42.733209208 -45.4204312 130.88685 -92.086150 177.55257
## 2004.5068 41.054938693 -47.3305145 129.44039 -94.118947 176.22882
## 2004.5096 44.189449636 -44.4272099 132.80611 -91.338036 179.71694
## 2004.5123 41.386382277 -47.4608820 130.23365 -94.493783 177.26655
## 2004.5151 44.201712728 -44.8755592 133.27898 -92.030219 180.43364
## 2004.5178 44.651345122 -44.6553422 133.95803 -91.931447 181.23414
## 2004.5205 44.605942933 -44.9295718 134.14146 -92.326810 181.53870
## 2004.5233 48.497565271 -41.2661937 138.26132 -88.784257 185.77939
## 2004.5260 45.842838874 -44.1485853 135.83426 -91.787168 183.47285
## 2004.5288 39.559759545 -50.6587554 129.77827 -98.417552 177.53707
## 2004.5315 41.407385733 -49.0376498 131.85242 -96.916360 179.73113
## 2004.5342 39.560096805 -51.1108934 130.23109 -99.109216 178.22941
## 2004.5370 45.239076060 -45.6573072 136.13546 -93.774946 184.25310
## 2004.5397 47.601998215 -43.5192205 138.72322 -91.755880 186.95988
## 2004.5425 45.688780016 -45.6567208 137.03428 -94.012108 185.38967
## 2004.5452 41.090575961 -50.4786576 132.65981 -98.952482 181.13363
## 2004.5479 43.840658663 -47.9517623 135.63308 -96.543735 184.22505
## 2004.5507 42.029909754 -49.9851572 134.04498 -98.694991 182.75481
## 2004.5534 39.946400242 -52.2907754 132.18358 -101.118187 181.01099
## 2004.5562 42.785532646 -49.6732181 135.24428 -98.617924 184.18899
## 2004.5589 45.742095564 -46.9377005 138.42189 -95.999421 187.48361
## 2004.5616 46.479949379 -46.4203661 139.38026 -95.598822 188.55872
## 2004.5644 43.312211479 -49.8081011 136.43252 -99.103017 185.72744
## 2004.5671 46.748265694 -46.5915256 140.08806 -96.002626 189.49916
## 2004.5699 46.623145196 -46.9356099 140.18190 -96.462623 189.70891
## 2004.5726 45.026144543 -48.7510630 138.80335 -98.393718 188.44601
## 2004.5753 49.308369024 -44.6867834 143.30352 -94.444811 193.06155
## 2004.5781 47.177318225 -47.0352748 141.38991 -96.908409 191.26305
## 2004.5808 42.916705440 -51.5128276 137.34624 -101.500803 187.33421
## 2004.5836 43.098293661 -51.5476820 137.74427 -101.650235 187.84682
## 2004.5863 48.683641685 -46.1782829 143.54557 -96.395152 193.76244
## 2004.5890 41.378801238 -53.6985817 136.45618 -104.029508 186.78711
## 2004.5918 44.955258976 -50.3370952 140.24761 -100.781820 190.69234
## 2004.5945 43.100584354 -52.4062571 138.60743 -102.964525 189.16569
## 2004.5973 46.191362991 -49.5294852 141.91221 -100.201041 192.58377
## 2004.6000 44.257539218 -51.6768383 140.19192 -102.461430 190.97651
## 2004.6027 45.428418126 -50.7190146 141.57585 -101.616391 192.47323
## 2004.6055 38.779893595 -57.5801231 135.13991 -108.590035 186.14982
## 2004.6082 45.010218435 -51.5619144 141.58235 -102.684113 192.70455
## 2004.6110 41.285909480 -55.4978746 138.06969 -106.732115 189.30393
## 2004.6137 40.936901892 -56.0580715 137.93188 -107.404109 189.27791
## 2004.6164 42.732183032 -54.4735209 139.93789 -105.931112 191.39548
## 2004.6192 45.859841518 -51.5561371 143.27582 -103.125041 194.84472
## 2004.6219 34.320962963 -63.3048374 131.94676 -114.984814 183.62674
## 2004.6247 35.642283249 -62.1928889 133.47746 -113.983701 185.26827
## 2004.6274 43.788809439 -54.2552874 141.83291 -106.156697 193.73432
## 2004.6301 44.793740485 -53.4588368 143.04632 -105.470609 195.05809
## 2004.6329 49.288972020 -49.1716443 147.74959 -101.293546 199.87149
## 2004.6356 50.716090367 -47.9521263 149.38431 -100.183925 201.61611
## 2004.6384 47.224855576 -51.6505255 146.10024 -103.991991 198.44170
## 2004.6411 46.456338311 -52.6257741 145.53845 -105.076676 197.98935
## 2004.6438 40.166301714 -59.1221116 139.45472 -111.682223 192.01483
## 2004.6466 42.185966022 -57.3083204 141.68025 -109.977414 194.34935
## 2004.6493 42.209535683 -57.4901987 141.90927 -110.268050 194.68712
## 2004.6521 35.276997548 -64.6277624 135.18176 -117.514148 188.06814
## 2004.6548 38.997354432 -61.1120111 139.10672 -114.106708 192.10142
## 2004.6575 37.603466932 -62.7100869 137.91702 -115.812875 191.01981
## 2004.6603 30.207151695 -70.3101756 130.72448 -123.520835 183.93514
## 2004.6630 38.083964152 -62.6367244 138.80465 -115.955036 192.12296
## 2004.6658 47.178725172 -53.7449149 148.10237 -107.170663 201.52811
## 2004.6685 32.241154504 -68.8850297 133.36734 -122.417998 186.90031
## 2004.6712 33.585687527 -67.7426360 134.91401 -121.382610 188.55399
## 2004.6740 35.348971078 -66.1810893 136.87903 -119.927857 190.62580
## 2004.6767 28.895892713 -72.8355045 130.62729 -126.688853 184.48064
## 2004.6795 32.704518445 -69.2278179 134.63685 -123.187537 188.59657
## 2004.6822 38.271817692 -63.8610624 140.40470 -117.926943 194.47058
## 2004.6849 32.153293441 -70.1797375 134.48632 -124.351572 188.65816
## 2004.6877 32.204105051 -70.3286859 134.73690 -124.606267 189.01448
## 2004.6904 31.611480098 -71.1206826 134.34364 -125.503804 188.72676
## 2004.6932 24.213046428 -78.7181017 127.14419 -133.206560 181.63265
## 2004.6959 16.710352058 -86.4193976 119.84010 -141.012989 174.43369
## 2004.6986 28.063565923 -75.2644036 131.39154 -129.962927 186.09006
## 2004.7014 19.911454185 -83.6143556 123.43726 -138.417609 178.24052
## 2004.7041 21.487171019 -82.2361017 125.21044 -137.143886 180.11823
## 2004.7068 27.696886174 -76.2234743 131.61725 -131.235590 186.62936
## 2004.7096 31.816808737 -72.3002664 135.93388 -127.416517 191.05013
## 2004.7123 25.896362044 -78.4170568 130.20978 -133.637245 185.42997
## 2004.7151 18.590424341 -85.9189693 123.09982 -141.242900 178.42375
## 2004.7178 5.793477291 -98.9115244 110.49848 -154.339004 165.92596
## 2004.7205 12.524404879 -92.3758401 117.42465 -147.906675 172.95549
## 2004.7233 24.209971195 -80.8851543 129.30510 -136.519153 184.93910
## 2004.7260 33.806593656 -71.4830517 139.09624 -127.220023 194.83321
## 2004.7288 29.925832856 -75.5579736 135.40964 -131.397728 191.24939
## 2004.7315 23.399205628 -82.2784053 129.07682 -138.220753 185.01916
## 2004.7342 29.103283202 -76.7677773 134.97434 -132.812531 191.01910
## 2004.7370 17.404858666 -88.6592987 123.46902 -144.806272 179.61599
## 2004.7397 21.505138907 -84.7517643 127.76204 -141.000771 184.01105
## 2004.7425 35.756576275 -70.6927239 142.20588 -127.043579 198.55673
## 2004.7452 31.339167345 -75.3021826 137.98052 -131.754703 194.43304
## 2004.7479 28.088568082 -78.7444864 134.92162 -135.298489 191.47563
## 2004.7507 21.794251503 -85.2301641 128.81867 -141.885467 185.47397
## 2004.7534 20.460183792 -86.7552514 127.67562 -143.511674 184.43204
## 2004.7562 22.781944749 -84.6241704 130.18806 -141.481533 187.04542
## 2004.7589 24.238186315 -83.3582708 131.83464 -140.316395 188.79277
## 2004.7616 29.278887962 -78.5075750 137.06535 -135.566282 194.12406
## 2004.7644 23.788320851 -84.1878136 131.76446 -141.346926 188.92357
## 2004.7671 20.985190714 -87.1802826 129.15066 -144.439625 186.41001
## 2004.7699 8.816776303 -99.5377051 117.17126 -156.897103 174.53066
## 2004.7726 14.985407920 -93.5577524 123.52857 -151.017031 180.98785
## 2004.7753 25.567823645 -83.1636882 134.29934 -140.722674 191.85832
## 2004.7781 18.990750478 -89.9287871 127.91029 -147.587307 185.56881
## 2004.7808 21.234797135 -87.8724423 130.34204 -145.630326 188.09992
## 2004.7836 17.992357761 -91.3022611 127.28698 -149.159337 185.14405
## 2004.7863 23.189046005 -86.2926315 132.67072 -144.248731 190.62682
## 2004.7890 7.451932932 -102.2164843 117.12035 -160.271437 175.17530
## 2004.7918 2.653757020 -107.2010824 112.50860 -165.354722 170.66224
## 2004.7945 6.007289643 -104.0336562 116.04824 -162.285814 174.30039
## 2004.7973 16.180030526 -94.0467075 126.40677 -152.397218 184.75728
## 2004.8000 20.120778622 -90.2914389 130.53300 -148.740136 188.98169
## 2004.8027 20.734260823 -89.8631252 131.33165 -148.409845 189.87837
## 2004.8055 15.708147188 -95.0740978 126.49039 -153.718676 185.13497
## 2004.8082 15.368723119 -95.5980729 126.33552 -154.340346 185.07779
## 2004.8110 24.070679693 -87.0803610 135.22172 -145.920168 194.06153
## 2004.8137 21.659312035 -89.6756683 132.99429 -148.612847 191.93147
## 2004.8164 13.556988671 -97.9616280 125.07561 -156.996018 184.11000
## 2004.8192 20.110699154 -91.5912519 131.81265 -150.722693 190.94409
## 2004.8219 9.234050999 -102.6509341 121.11904 -161.879267 180.34737
## 2004.8247 13.105201055 -98.9625191 125.17292 -158.287587 184.49799
## 2004.8274 14.277208773 -97.9729490 126.52737 -157.394593 185.94901
## 2004.8301 17.026515479 -95.4057838 129.45881 -154.923848 188.97688
## 2004.8329 21.084056041 -91.5300902 133.69820 -151.144418 193.31253
## 2004.8356 5.349270103 -107.4464300 118.14497 -167.156867 177.85541
## 2004.8384 -2.109429416 -115.0863915 110.86753 -174.892783 170.67392
## 2004.8411 23.061021235 -90.0969126 136.21896 -149.999104 196.12115
## 2004.8438 28.751757721 -84.5868588 142.09037 -144.584698 202.08821
## 2004.8466 15.765399564 -97.7536121 129.28441 -157.846947 189.37775
## 2004.8493 10.873204646 -102.8259160 124.57233 -163.014595 184.76100
## 2004.8521 -8.822743830 -122.7016885 105.05620 -182.985560 165.34007
## 2004.8548 1.454257606 -112.6042276 115.51274 -172.983142 175.89166
## 2004.8575 10.643375125 -103.5943685 124.88112 -164.068177 185.35493
## 2004.8603 20.132413449 -94.2843077 134.54913 -154.852861 195.11769
## 2004.8630 30.246725480 -84.3486937 144.84214 -145.011844 205.50530
## 2004.8658 10.456461603 -104.3173773 125.23030 -165.074978 185.98790
## 2004.8685 10.121403216 -104.8305786 125.07339 -165.682482 185.92529
## 2004.8712 5.399322151 -109.7305269 120.52917 -170.676587 181.47523
## 2004.8740 13.395743794 -101.9116981 128.70319 -162.951771 189.74326
## 2004.8767 21.568312328 -93.9164493 137.05307 -155.050389 198.18701
## 2004.8795 16.667305525 -98.9945040 132.32912 -160.222167 193.55678
## 2004.8822 7.104670768 -108.7339160 122.94326 -170.055160 184.26450
## 2004.8849 11.588398610 -104.4266961 127.60349 -165.841377 189.01817
## 2004.8877 20.951828608 -95.2395059 137.14316 -156.747483 198.65114
## 2004.8904 19.720259780 -96.6470476 136.08757 -158.248179 197.68870
## 2004.8932 13.480305592 -103.0627090 130.02332 -164.756854 191.71747
## 2004.8959 6.037908877 -110.6805483 122.75637 -172.467567 184.54339
## 2004.8986 4.982663514 -111.9109730 121.87630 -173.790726 183.75605
## 2004.9014 -0.007340235 -117.0758940 117.06121 -179.048243 179.03356
## 2004.9041 17.584333165 -99.6588769 134.82754 -161.723683 196.89235
## 2004.9068 14.042840404 -103.3747661 131.46045 -165.531892 193.61757
## 2004.9096 0.193688408 -117.3980559 117.78543 -179.647365 180.03474
## 2004.9123 21.487598717 -96.2780259 139.25322 -158.619382 201.59458
## 2004.9151 35.502002978 -82.4372456 153.44125 -144.870512 215.87452
## 2004.9178 15.264535242 -102.8480820 133.37715 -165.373125 195.90220
## 2004.9205 13.287041452 -104.9986905 131.57277 -167.615375 194.18946
## 2004.9233 15.019356383 -103.4392372 133.47795 -166.147429 196.18614
## 2004.9260 10.462744577 -108.1684587 129.09395 -170.968024 191.89351
## 2004.9288 1.258169717 -117.5453926 120.06173 -180.436200 182.95254
## 2004.9315 4.015259069 -114.9604125 122.99093 -177.942329 185.97285
## 2004.9342 -17.337199570 -136.4847318 101.81033 -199.557625 164.88323
## 2004.9370 8.805058380 -110.5140870 128.12420 -173.677827 191.28794
## 2004.9397 22.703273752 -96.7872383 142.19379 -160.041694 205.44824
## 2004.9425 19.439372424 -100.2222609 139.10101 -163.567303 202.44605
## 2004.9452 8.365092064 -111.4674181 128.19760 -174.902917 191.63310
## 2004.9479 9.364797592 -110.6383462 129.36794 -174.164173 192.89377
## 2004.9507 17.513970255 -102.6595648 137.68751 -166.275591 201.30353
## 2004.9534 13.649091017 -106.6945941 133.99278 -170.400693 197.69887
## 2004.9562 16.359238260 -104.1543566 136.87283 -167.950400 200.66888
## 2004.9589 8.315842121 -112.3674233 128.99911 -176.253285 192.88497
## 2004.9616 11.913976055 -108.9387218 132.76667 -172.914276 196.74223
## 2004.9644 17.207938518 -103.8139545 138.22983 -167.879075 202.29495
## 2004.9671 15.218028182 -105.9728238 136.40888 -170.127386 200.56344
## 2004.9699 2.446018792 -118.9135569 123.80559 -183.157436 188.04947
## 2004.9726 6.112418176 -115.4156470 127.64048 -179.748719 191.97356
## 2004.9753 5.659208178 -116.0371132 127.35553 -180.459254 191.77767
## 2004.9781 3.537272747 -118.3270726 125.40162 -182.838160 189.91271
## 2004.9808 10.089589069 -111.9425488 132.12173 -176.542460 196.72164
## 2004.9836 12.231175991 -109.9685240 134.43088 -174.657138 199.11949
## 2004.9863 16.863428571 -105.5036042 139.23046 -170.280798 204.00766
## 2004.9890 15.401866603 -107.1322703 137.93600 -171.997924 202.80166
## 2004.9918 -1.723815351 -124.4248289 120.97720 -189.378822 185.93119
## 2004.9945 11.778424288 -111.0892392 134.64609 -176.131451 199.68830
## 2004.9973 13.395149732 -109.6389380 136.42924 -174.769250 201.55955
## 2005.0000 11.403125811 -111.7971614 134.60341 -177.015454 199.82171
## 2005.0027 32.225373152 -91.1408896 155.59164 -156.447044 220.89779
## 2005.0055 16.897052145 -106.6349631 140.42907 -172.028862 205.82297
## 2005.0082 18.880269119 -104.8172766 142.57781 -170.298802 208.05934
## 2005.0110 28.090116005 -95.7727389 151.95297 -161.341774 217.52201
## 2005.0137 27.992483454 -96.0354603 152.02043 -161.691888 217.67685
## 2005.0164 31.624741870 -92.5680713 155.81756 -158.311775 221.56126
## 2005.0192 9.096112091 -115.2613519 133.45358 -181.092217 199.28444
## 2005.0219 15.296380701 -109.2255165 139.81828 -175.143427 205.73619
## 2005.0247 20.648317134 -104.0377963 145.33443 -170.042638 211.33927
## 2005.0274 8.434968649 -116.4151451 133.28508 -182.506803 199.37674
## 2005.0301 21.361635444 -103.6522634 146.37553 -169.830624 212.55389
## 2005.0329 11.016897487 -114.1605722 136.19437 -180.425522 202.45932
## 2005.0356 13.634269363 -111.7065578 138.97510 -178.057984 205.32652
## 2005.0384 20.632098920 -104.8718730 146.13607 -171.309662 212.57386
## 2005.0411 24.126739699 -101.5401651 149.79364 -168.064206 216.31769
## 2005.0438 30.134130746 -95.6954961 155.96376 -162.305677 222.57394
## 2005.0466 11.517810221 -114.4743284 137.50995 -181.170538 204.20616
## 2005.0493 22.387615713 -103.7668254 148.54206 -170.548953 215.32418
## 2005.0521 17.013288253 -109.3032468 143.32982 -176.171181 210.19776
## 2005.0548 6.557020871 -119.9214004 133.03544 -186.875032 199.98907
## 2005.0575 2.741376067 -123.8987244 129.38148 -190.937944 196.42070
## 2005.0603 17.059782153 -109.7417914 143.86136 -176.866490 210.98605
## 2005.0630 10.029250521 -116.9335908 136.99209 -184.143659 204.20216
## 2005.0658 23.029083963 -104.0948205 150.15299 -171.390151 217.44832
## 2005.0685 15.985678246 -111.2990856 143.27044 -178.679569 210.65093
## 2005.0712 1.538199489 -125.9072207 128.98362 -193.372751 196.44915
## 2005.0740 5.807256382 -121.7986178 133.41313 -189.349087 200.96360
## 2005.0767 15.671677248 -112.0944495 143.43780 -179.729751 211.07311
## 2005.0795 23.767774695 -104.1584039 151.69395 -171.878432 219.41398
## 2005.0822 23.278159899 -104.8078705 151.36419 -172.612519 219.16884
## 2005.0849 27.079270172 -101.1664127 155.32495 -169.055576 223.21412
## 2005.0877 17.181044951 -111.2240920 145.58618 -179.197666 213.55976
## 2005.0904 18.056181698 -110.5082116 146.62057 -178.566090 214.67845
## 2005.0932 28.264400931 -100.4590516 156.98785 -168.601131 225.12993
## 2005.0959 11.362886107 -117.5194294 140.24520 -185.745606 208.47138
## 2005.0986 11.615294457 -117.4256884 140.65628 -185.735858 208.96645
## 2005.1014 7.139396851 -122.0600585 136.33885 -190.454119 204.73291
## 2005.1041 9.188190800 -120.1695429 138.54592 -188.647391 207.02377
## 2005.1068 12.833606304 -116.6822124 142.34943 -185.243745 210.91096
## 2005.1096 25.168002869 -104.5057081 154.84171 -173.150824 223.48683
## 2005.1123 14.887916867 -114.9434943 144.71933 -183.672092 213.44793
## 2005.1151 20.562243332 -109.4266767 150.55116 -178.238654 219.36314
## 2005.1178 26.142123528 -104.0041148 156.28836 -172.899372 225.18362
## 2005.1205 20.450762835 -109.8526038 150.75413 -178.831039 219.73257
## 2005.1233 0.216738388 -130.2435674 130.67704 -199.305082 199.73856
## 2005.1260 9.690306711 -120.9267496 140.30736 -190.071242 209.45186
## 2005.1288 16.795142737 -113.9784762 147.56876 -183.205848 216.79613
## 2005.1315 21.157622359 -109.7723720 152.08762 -179.082524 221.39777
## 2005.1342 26.046995187 -105.0391880 157.13318 -174.432022 226.52601
## 2005.1370 11.236546173 -120.0056400 142.47873 -189.481057 211.95415
## 2005.1397 5.522144366 -125.8758596 136.92015 -195.433761 206.47805
## 2005.1425 14.397208105 -117.1564291 145.95085 -186.796718 215.59113
## 2005.1452 21.080217937 -110.6288686 152.78930 -180.351447 222.51188
## 2005.1479 23.120652307 -108.7437003 154.98500 -178.548472 224.78978
## 2005.1507 33.447796921 -98.5716392 165.46723 -168.458507 235.35410
## 2005.1534 18.657029080 -113.5173085 150.83137 -183.486176 220.80023
## 2005.1562 21.856864632 -110.4721932 154.18592 -180.522965 224.23669
## 2005.1589 23.957806403 -108.5257909 156.44140 -178.658371 226.57398
## 2005.1616 3.181118701 -129.4568380 135.81908 -199.671131 206.03337
## 2005.1644 18.756933734 -114.0352030 151.54907 -184.331114 221.84498
## 2005.1671 27.941333934 -105.0048040 160.88747 -175.382238 231.26491
## 2005.1699 15.563827832 -117.5361331 148.66379 -187.994996 219.12265
## 2005.1726 24.900626317 -108.3529801 158.15423 -178.893178 228.69443
## 2005.1753 27.526303523 -105.8807714 160.93338 -176.502211 231.55482
## 2005.1781 20.273941434 -113.2864256 153.83431 -183.989013 224.53690
## 2005.1808 26.248734579 -107.4647489 159.96222 -178.248391 230.74586
## 2005.1836 3.257296699 -130.6091280 137.12372 -201.473733 207.98833
## 2005.1863 12.061090960 -121.9581005 146.08028 -192.903575 217.02576
## 2005.1890 8.170267190 -126.0015171 142.34205 -197.027769 213.36830
## 2005.1918 3.072079221 -131.2521245 137.39628 -202.359063 208.50322
## 2005.1945 11.653018862 -122.8234316 146.12947 -194.010964 217.31700
## 2005.1973 33.228386511 -101.4001385 167.85691 -172.668175 239.12495
## 2005.2000 32.140889334 -102.6395386 166.92132 -173.987987 238.26977
## 2005.2027 30.786462367 -104.1456975 165.71862 -175.574468 237.14739
## 2005.2055 31.110109544 -103.9736118 166.19383 -175.482614 237.70283
## 2005.2082 30.641157178 -104.5939558 165.87627 -176.183100 237.46541
## 2005.2110 25.329533742 -110.0568016 160.71587 -181.725998 232.38507
## 2005.2137 16.523344042 -119.0140450 152.06073 -190.763205 223.80989
## 2005.2164 9.586450044 -126.1018244 145.27472 -197.930858 217.10376
## 2005.2192 19.410752563 -116.4282398 155.24974 -188.337059 227.15856
## 2005.2219 23.876615298 -112.1129279 159.86616 -184.101444 231.85467
## 2005.2247 21.821187669 -114.3187399 157.96112 -186.386864 230.02924
## 2005.2274 18.978814332 -117.3113316 155.26896 -189.458977 227.41661
## 2005.2301 17.711127243 -118.7290717 154.15133 -190.956150 226.37840
## 2005.2329 21.437896663 -115.1521905 158.02798 -187.458615 230.33441
## 2005.2356 15.009968468 -121.7298426 151.74978 -194.115526 224.13546
## 2005.2384 15.524562989 -121.3648082 152.41393 -193.829664 224.87879
## 2005.2411 22.006507138 -115.0322609 159.04528 -187.576203 231.58922
## 2005.2438 35.635903579 -101.5520987 172.82391 -174.175040 245.44685
## 2005.2466 35.555339075 -101.7817352 172.89241 -174.483591 245.59427
## 2005.2493 31.097412158 -106.3885726 168.58340 -179.169257 241.36408
## 2005.2521 25.441565485 -112.1931685 163.07630 -185.052596 235.93573
## 2005.2548 27.923390201 -109.8599325 165.70671 -182.798018 238.64480
## 2005.2575 21.818113088 -116.1136383 159.74986 -189.130297 232.76652
## 2005.2603 21.534438272 -116.5455822 159.61446 -189.640730 232.70961
## 2005.2630 12.810555548 -125.4175750 151.03869 -198.591127 224.21224
## 2005.2658 16.354598160 -122.0214839 154.73068 -195.273357 227.98255
## 2005.2685 19.427540035 -119.0963355 157.95142 -192.426446 231.28153
## 2005.2712 11.308935208 -127.3625763 149.98045 -200.770840 223.38871
## 2005.2740 19.022002118 -119.7969884 157.84099 -193.283323 231.32733
## 2005.2767 22.620740603 -116.3455723 161.58705 -189.909895 235.15138
## 2005.2795 19.332448425 -119.7810309 158.44593 -193.423259 232.08816
## 2005.2822 22.258524969 -117.0019653 161.51902 -190.722016 235.23907
## 2005.2849 20.695403209 -118.7119430 160.10275 -192.509734 233.90054
## 2005.2877 25.110437113 -114.4436104 164.66448 -188.319061 238.53993
## 2005.2904 18.499860579 -121.2007343 158.20046 -195.153762 232.15348
## 2005.2932 27.318672138 -112.5283164 167.16566 -186.558840 241.19618
## 2005.2959 25.171313154 -114.8219161 165.16454 -188.929855 239.27248
## 2005.2986 28.934201197 -111.2051160 169.07352 -185.390389 243.25879
## 2005.3014 34.177254659 -106.1079985 174.46251 -180.370526 248.72503
## 2005.3041 35.553088310 -104.8779491 175.98413 -179.217650 250.32383
## 2005.3068 29.925706452 -110.6509640 170.50238 -185.067758 244.91917
## 2005.3096 29.774574870 -110.9475779 170.49673 -185.441386 244.99054
## 2005.3123 32.551928949 -108.3155560 173.41941 -182.886298 247.99016
## 2005.3151 23.771052765 -117.2416145 164.78372 -191.889211 239.43132
## 2005.3178 28.722123390 -112.4355768 169.87982 -187.159950 244.60420
## 2005.3205 27.549865731 -113.7527186 168.85245 -188.553788 243.65352
## 2005.3233 29.630800512 -111.8165196 171.07812 -186.694208 245.95581
## 2005.3260 32.205083273 -109.3868246 173.79699 -184.341053 248.75122
## 2005.3288 41.492567330 -100.2437808 183.22892 -175.274471 258.25961
## 2005.3315 20.751188140 -121.1294532 162.63183 -196.236528 237.73890
## 2005.3342 16.391298097 -125.6334899 158.41609 -200.816871 233.59947
## 2005.3370 26.704841424 -115.4639471 168.87363 -190.723558 244.13324
## 2005.3397 34.553941744 -107.7587015 176.86659 -183.094464 252.20235
## 2005.3425 28.944217190 -113.5121356 171.40057 -188.923973 246.81241
## 2005.3452 17.901484484 -124.6984330 160.50140 -200.186269 235.98924
## 2005.3479 22.485112991 -120.2582248 165.22845 -195.821983 240.79221
## 2005.3507 27.928351721 -114.9582624 170.81497 -190.597867 246.45457
## 2005.3534 31.728469752 -111.3012772 174.75822 -187.016652 250.47359
## 2005.3562 24.050082740 -119.1226539 167.22282 -194.913723 243.01389
## 2005.3589 17.332488140 -125.9830956 160.64807 -201.849783 236.51476
## 2005.3616 35.988474233 -107.4698143 179.44676 -183.412045 255.38899
## 2005.3644 33.311461768 -110.2893898 176.91231 -186.307089 252.93001
## 2005.3671 36.063841227 -107.6794319 179.80711 -183.772524 255.90021
## 2005.3699 37.097667261 -106.7878865 180.98322 -182.956298 257.15163
## 2005.3726 33.890052530 -110.1376413 177.91775 -186.381297 254.16140
## 2005.3753 33.822035091 -110.3476587 177.99173 -186.666485 254.31055
## 2005.3781 39.122967691 -105.1885863 183.43452 -181.582508 259.82844
## 2005.3808 31.887385312 -112.5658896 176.34066 -189.034834 252.80960
## 2005.3836 29.728702897 -114.8661540 174.32356 -191.410048 250.86745
## 2005.3863 37.576462720 -107.1598377 182.31276 -183.778607 258.93153
## 2005.3890 43.975799615 -100.9018063 188.85341 -177.595378 265.54698
## 2005.3918 42.640092152 -102.3786814 187.65887 -179.146983 264.42717
## 2005.3945 45.603734909 -99.5560691 190.76354 -176.399028 267.60650
## 2005.3973 39.861609121 -105.4390885 185.16231 -182.356632 262.07985
## 2005.4000 43.412981891 -102.0284728 188.85444 -179.020528 265.84649
## 2005.4027 43.252170442 -102.3299052 188.83425 -179.396401 265.90074
## 2005.4055 42.944751885 -102.7778090 188.66731 -179.918673 265.80818
## 2005.4082 41.492540116 -104.3703708 187.35545 -181.585532 264.57061
## 2005.4110 27.178755978 -118.8243700 173.18188 -196.113756 250.47127
## 2005.4137 34.293002690 -111.8502038 180.43621 -189.213744 257.79975
## 2005.4164 38.828027126 -107.4551258 185.11118 -184.892749 262.54880
## 2005.4192 39.497738061 -106.9252275 185.92070 -184.436863 263.43234
## 2005.4219 39.711596473 -106.8510483 186.27424 -184.436626 263.85982
## 2005.4247 41.821443892 -104.8807472 188.52363 -182.540196 266.18308
## 2005.4274 36.044075517 -110.7975292 182.88568 -188.530779 260.61893
## 2005.4301 38.806536470 -108.1743497 185.78742 -185.981331 263.59440
## 2005.4329 40.170682144 -106.9493535 187.29072 -184.829996 265.17136
## 2005.4356 42.061120990 -105.1979328 189.32017 -183.152167 267.27441
## 2005.4384 39.013398331 -108.3845424 186.41134 -186.412299 264.43910
## 2005.4411 38.717526259 -108.8191707 186.25422 -186.920380 264.35543
## 2005.4438 34.694809351 -112.9805134 182.37013 -191.155107 260.54473
## 2005.4466 37.662174380 -110.1516442 185.47599 -188.399553 263.72390
## 2005.4493 42.324875840 -105.6273089 190.27706 -183.948465 268.59822
## 2005.4521 42.198619564 -105.8918021 190.28904 -184.286136 268.68338
## 2005.4548 46.406600309 -101.8219294 194.63513 -180.289373 273.10257
## 2005.4575 44.969034997 -103.3974741 193.33554 -181.937960 271.87603
## 2005.4603 45.215619306 -103.2887410 193.71998 -181.902201 272.33344
## 2005.4630 42.968289598 -105.6737941 191.61037 -184.360160 270.29674
## 2005.4658 45.748242120 -103.0314375 194.52792 -181.790642 273.28713
## 2005.4685 48.471860603 -100.4452878 197.38901 -179.277264 276.22099
## 2005.4712 45.264923321 -103.7895670 194.31941 -182.694248 273.22409
## 2005.4740 40.707023148 -108.4846827 189.89873 -187.462001 268.87605
## 2005.4767 45.016585865 -104.3122095 194.34538 -183.362099 273.39527
## 2005.4795 43.779324149 -105.6864349 193.24508 -184.808828 272.36748
## 2005.4822 42.515374428 -107.0872229 192.11797 -186.282054 271.31280
## 2005.4849 47.167778390 -102.5715323 196.90709 -181.838735 276.17429
## 2005.4877 44.471918307 -105.4039809 194.34782 -184.743489 273.68733
## 2005.4904 41.854779220 -108.1575842 191.86714 -187.569333 271.27889
## 2005.4932 40.830191753 -109.3185119 190.97890 -188.802434 270.46282
## 2005.4959 42.637000372 -107.6479197 192.92192 -187.203951 272.47795
## 2005.4986 45.639852491 -104.7811607 196.06087 -184.409235 275.68894
## 2005.5014 45.747153980 -104.8098294 196.30414 -184.509882 276.00419
## 2005.5041 42.733209208 -107.9596216 193.42604 -187.731588 273.19801
## 2005.5068 41.054938693 -109.7736172 191.88349 -189.617432 271.72731
## 2005.5096 44.189449636 -106.7747093 195.15361 -186.690308 275.06921
## 2005.5123 41.386382277 -109.7132580 192.48602 -189.700576 272.47334
## 2005.5151 44.201712728 -107.0332875 195.43671 -187.092261 275.49569
## 2005.5178 44.651345122 -106.7188941 196.02158 -186.849458 276.15215
## 2005.5205 44.605942933 -106.8994145 196.11130 -187.101506 276.31339
## 2005.5233 48.497565271 -103.1427900 200.13792 -183.416345 280.41148
## 2005.5260 45.842838874 -105.9323941 197.61807 -186.277349 277.96303
## 2005.5288 39.559759545 -112.3502315 191.46975 -192.766523 271.88604
## 2005.5315 41.407385733 -110.6372438 193.45202 -191.124809 273.93958
## 2005.5342 39.560096805 -112.6190522 191.73925 -193.177828 272.29802
## 2005.5370 45.239076060 -107.0744736 197.55263 -187.704396 278.18255
## 2005.5397 47.601998215 -104.8458336 200.04983 -185.546841 280.75084
## 2005.5425 45.688780016 -106.8932158 198.27078 -187.665245 279.04281
## 2005.5452 41.090575961 -111.6254659 193.80662 -192.468455 274.64961
## 2005.5479 43.840658663 -109.0093118 196.69063 -189.923198 277.60452
## 2005.5507 42.029909754 -110.9538720 195.01369 -191.938594 275.99841
## 2005.5534 39.946400242 -113.1710759 193.06388 -194.226572 274.11937
## 2005.5562 42.785532646 -110.4655212 196.03659 -191.591729 277.16279
## 2005.5589 45.742095564 -107.6424197 199.12661 -188.839277 280.32347
## 2005.5616 46.479949379 -107.0379113 199.99781 -188.305358 281.26526
## 2005.5644 43.312211479 -110.3388788 196.96330 -191.676853 278.30128
## 2005.5671 46.748265694 -107.0359388 200.53247 -188.444379 281.94091
## 2005.5699 46.623145196 -107.2940584 200.54035 -188.772904 282.01919
## 2005.5726 45.026144543 -109.0239434 199.07623 -190.573134 280.62542
## 2005.5753 49.308369024 -104.8744886 203.49123 -186.493963 285.11070
## 2005.5781 47.177318225 -107.1381950 201.49283 -188.827893 283.18253
## 2005.5808 42.916705440 -111.5313493 197.36476 -193.291211 279.12462
## 2005.5836 43.098293661 -111.4821891 197.67878 -193.312154 279.50874
## 2005.5863 48.683641685 -106.0291556 203.39644 -187.929163 285.29645
## 2005.5890 41.378801238 -113.4661976 196.22380 -195.436189 278.19379
## 2005.5918 44.955258976 -110.0218286 199.93235 -192.061743 281.97226
## 2005.5945 43.100584354 -112.0084795 198.20965 -194.118258 280.31943
## 2005.5973 46.191362991 -109.0495649 201.43229 -191.229148 283.61187
## 2005.6000 44.257539218 -111.1151409 199.63022 -193.364469 281.87955
## 2005.6027 45.428418126 -110.0759025 200.93274 -192.394917 283.25175
## 2005.6055 38.779893595 -116.8559562 194.41574 -199.244598 276.80439
## 2005.6082 45.010218435 -110.7570495 200.77749 -193.215260 283.23570
## 2005.6110 41.285909480 -114.6126658 197.18448 -197.140386 279.71221
## 2005.6137 40.936901892 -115.0928702 196.96667 -197.690042 279.56385
## 2005.6164 42.732183032 -113.4286757 198.89304 -196.095241 281.55961
## 2005.6192 45.859841518 -110.4319939 202.15168 -193.167894 284.88758
## 2005.6219 34.320962963 -122.1017394 190.74367 -204.906916 273.54884
## 2005.6247 35.642283249 -120.9111768 192.19574 -203.785572 275.07014
## 2005.6274 43.788809439 -112.8952991 200.47292 -195.838856 283.41647
## 2005.6301 44.793740485 -112.0209076 201.60839 -195.033568 284.62105
## 2005.6329 49.288972020 -107.6561072 206.23405 -190.737814 289.31576
## 2005.6356 50.716090367 -106.3593116 207.79149 -189.510007 290.94219
## 2005.6384 47.224855576 -109.9807611 204.43047 -193.200388 287.65010
## 2005.6411 46.456338311 -110.8793853 203.79206 -194.167886 287.08056
## 2005.6438 40.166301714 -117.2994213 197.63202 -200.656740 280.98934
## 2005.6466 42.185966022 -115.4096492 199.78158 -198.835729 283.20766
## 2005.6493 42.209535683 -115.5158648 199.93494 -199.010648 283.42972
## 2005.6521 35.276997548 -122.5780815 193.13208 -206.141513 276.69551
## 2005.6548 38.997354432 -118.9872967 196.98201 -202.619319 280.61403
## 2005.6575 37.603466932 -120.5106501 195.71758 -204.211208 279.41814
## 2005.6603 30.207151695 -128.0363253 188.45063 -211.805362 272.21967
## 2005.6630 38.083964152 -120.2887672 196.45670 -204.126227 280.29416
## 2005.6658 47.178725172 -111.3231551 205.68061 -195.228982 289.58643
## 2005.6685 32.241154504 -126.3897695 190.87208 -210.363908 274.84622
## 2005.6712 33.585687527 -125.1741754 192.34555 -209.216570 276.38795
## 2005.6740 35.348971078 -123.5397261 194.23767 -207.650322 278.34826
## 2005.6767 28.895892713 -130.1215343 187.91332 -214.300275 272.09206
## 2005.6795 32.704518445 -126.4415343 191.85057 -210.688366 276.09740
## 2005.6822 38.271817692 -121.0027569 197.54639 -205.317624 281.86126
## 2005.6849 32.153293441 -127.2496994 191.55629 -211.632547 275.93913
## 2005.6877 32.204105051 -127.3272027 191.73541 -211.777976 276.18619
## 2005.6904 31.611480098 -128.0480394 191.27100 -212.566684 275.78964
## 2005.6932 24.213046428 -135.5745819 184.00067 -220.161043 268.58714
## 2005.6959 16.710352058 -143.2052826 176.62599 -227.859506 261.28021
## 2005.6986 28.063565923 -131.9799725 188.10710 -216.701904 272.82904
## 2005.7014 19.911454185 -140.2598860 180.08279 -225.049472 264.87238
## 2005.7041 21.487171019 -138.8118690 181.78621 -223.669055 266.64340
## 2005.7068 27.696886174 -132.7297520 188.12352 -217.654484 273.04826
## 2005.7096 31.816808737 -128.7373262 192.37094 -213.729551 277.36317
## 2005.7123 25.896362044 -134.7851686 186.57789 -219.844833 271.63756
## 2005.7151 18.590424341 -142.2184009 179.39925 -227.345451 264.52630
## 2005.7178 5.793477291 -155.1425420 166.72950 -240.336924 251.92388
## 2005.7205 12.524404879 -148.5387080 173.58752 -233.800370 258.84918
## 2005.7233 24.209971195 -136.9801350 185.40008 -222.309023 270.72897
## 2005.7260 33.806593656 -127.5104059 195.12359 -212.906467 280.51965
## 2005.7288 29.925832856 -131.5179603 191.36963 -216.981142 276.83281
## 2005.7315 23.399205628 -138.1712817 184.96969 -223.701531 270.49994
## 2005.7342 29.103283202 -132.5937990 190.80037 -218.191064 276.39763
## 2005.7370 17.404858666 -144.4187193 179.22844 -230.082947 264.89266
## 2005.7397 21.505138907 -140.4448361 183.45511 -226.175974 269.18625
## 2005.7425 35.756576275 -126.3196972 197.83285 -212.117694 283.63085
## 2005.7452 31.339167345 -130.8633062 193.54164 -216.728109 279.40644
## 2005.7479 28.088568082 -134.2400075 190.41714 -220.171565 276.34870
## 2005.7507 21.794251503 -140.6603282 184.24883 -226.658588 270.24709
## 2005.7534 20.460183792 -142.1203024 183.04067 -228.185213 269.10558
## 2005.7562 22.781944749 -139.9243504 185.48824 -226.055860 271.61975
## 2005.7589 24.238186315 -138.5938207 187.07019 -224.791878 273.26825
## 2005.7616 29.278887962 -133.6787339 192.23651 -219.943288 278.50106
## 2005.7644 23.788320851 -139.2948191 186.87146 -225.625819 273.20246
## 2005.7671 20.985190714 -142.2233708 184.19375 -228.620764 270.59115
## 2005.7699 8.816776303 -154.5171104 172.15066 -240.980847 258.61440
## 2005.7726 14.985407920 -148.4737080 178.44452 -235.003737 264.97455
## 2005.7753 25.567823645 -138.0164256 189.15207 -224.612696 275.74834
## 2005.7781 18.990750478 -144.7185364 182.70004 -231.380998 269.36250
## 2005.7808 21.234797135 -142.5994319 185.06903 -229.328034 271.79763
## 2005.7836 17.992357761 -145.9667183 181.95143 -232.761410 268.74613
## 2005.7863 23.189046005 -140.8947821 187.27287 -227.755514 274.13361
## 2005.7890 7.451932932 -156.7565524 171.66042 -243.683274 258.58714
## 2005.7918 2.653757020 -161.6792910 166.98681 -248.671952 253.97947
## 2005.7945 6.007289643 -158.4502267 170.46481 -245.508777 257.52336
## 2005.7973 16.180030526 -148.4018600 180.76192 -235.526250 267.88631
## 2005.8000 20.120778622 -144.5853922 184.82695 -231.775572 272.01713
## 2005.8027 20.734260823 -144.0960966 185.56462 -231.352017 272.82054
## 2005.8055 15.708147188 -149.2463033 180.66260 -236.567915 267.98421
## 2005.8082 15.368723119 -149.7097272 180.44717 -237.096980 267.83443
## 2005.8110 24.070679693 -141.1316773 189.27304 -228.584522 276.72588
## 2005.8137 21.659312035 -143.6668588 186.98548 -231.185247 274.50387
## 2005.8164 13.556988671 -151.8929034 179.00688 -239.476786 266.59076
## 2005.8192 20.110699154 -145.4628217 185.68422 -233.112149 273.33355
## 2005.8219 9.234050999 -156.4630063 174.93111 -244.177730 262.64583
## 2005.8247 13.105201055 -152.7153008 178.92570 -240.495372 266.70577
## 2005.8274 14.277208773 -151.6666457 180.22106 -239.512016 268.06643
## 2005.8301 17.026515479 -149.0406000 183.09363 -236.951221 271.00425
## 2005.8329 21.084056041 -145.1062291 187.27434 -233.082052 275.25016
## 2005.8356 5.349270103 -160.9640934 171.66263 -249.005070 259.70361
## 2005.8384 -2.109429416 -168.5457803 164.32692 -256.651862 252.43300
## 2005.8411 23.061021235 -143.4982262 189.62027 -231.669366 277.79141
## 2005.8438 28.751757721 -137.9302957 195.43381 -226.166445 283.66996
## 2005.8466 15.765399564 -151.0393694 182.57017 -239.340480 270.87128
## 2005.8493 10.873204646 -156.0541896 177.80060 -244.420214 266.16662
## 2005.8521 -8.822743830 -175.8726734 158.22719 -264.303564 246.65808
## 2005.8548 1.454257606 -165.7181174 168.62663 -254.213827 257.12234
## 2005.8575 10.643375125 -156.6513558 177.93811 -245.211837 266.49859
## 2005.8603 20.132413449 -147.2845839 187.54941 -235.909789 276.17462
## 2005.8630 30.246725480 -137.2924491 197.78590 -225.982331 286.47578
## 2005.8658 10.456461603 -157.2048012 178.11772 -245.959312 266.87224
## 2005.8685 10.121403216 -157.6618589 177.90467 -246.480953 266.72376
## 2005.8712 5.399322151 -162.5058507 173.30449 -251.389480 262.18812
## 2005.8740 13.395743794 -154.6312513 181.42274 -243.579370 270.37086
## 2005.8767 21.568312328 -146.5804167 189.71704 -235.592977 278.72960
## 2005.8795 16.667305525 -151.6030695 184.93768 -240.680025 274.01464
## 2005.8822 7.104670768 -161.2872623 175.49660 -250.428567 264.63791
## 2005.8849 11.588398610 -156.9250048 180.10180 -246.130612 269.30741
## 2005.8877 20.951828608 -147.6829577 189.58661 -236.952821 278.85648
## 2005.8904 19.720259780 -149.0358220 188.47634 -238.369895 277.81042
## 2005.8932 13.480305592 -155.3969847 182.35760 -244.795222 271.75583
## 2005.8959 6.037908877 -162.9605029 175.03632 -252.422858 264.49868
## 2005.8986 4.982663514 -164.1367830 174.10211 -253.663210 263.62854
## 2005.9014 -0.007340235 -169.2477350 169.23305 -258.838188 258.82351
## 2005.9041 17.584333165 -151.7769234 186.94559 -241.431357 276.60002
## 2005.9068 14.042840404 -155.4391918 183.52487 -245.157560 273.24324
## 2005.9096 0.193688408 -169.4090334 169.79641 -259.191291 259.57867
## 2005.9123 21.487598717 -148.2357269 191.21092 -238.081828 281.05703
## 2005.9151 35.502002978 -134.3418408 205.34585 -224.251741 295.25575
## 2005.9178 15.264535242 -154.6997413 185.22881 -244.673394 275.20246
## 2005.9205 13.287041452 -156.7975825 183.37167 -246.834944 273.40903
## 2005.9233 15.019356383 -155.1855299 185.22424 -245.286554 275.32527
## 2005.9260 10.462744577 -159.8623191 180.78781 -250.026961 270.95245
## 2005.9288 1.258169717 -169.1869867 171.70333 -259.415202 261.93154
## 2005.9315 4.015259069 -166.5499055 174.58042 -256.841649 264.87217
## 2005.9342 -17.337199570 -188.0222879 153.34789 -278.377516 243.70312
## 2005.9370 8.805058380 -161.9998695 179.60999 -252.418537 270.02865
## 2005.9397 22.703273752 -148.2214096 193.62796 -238.703471 284.11002
## 2005.9425 19.439372424 -151.6049827 190.48373 -242.150395 281.02914
## 2005.9452 8.365092064 -162.7988510 179.52904 -253.407569 270.13775
## 2005.9479 9.364797592 -161.9186500 180.64825 -252.590630 271.32023
## 2005.9507 17.513970255 -153.8888986 188.91684 -244.624096 279.65204
## 2005.9534 13.649091017 -157.8731159 185.17130 -248.671488 275.96967
## 2005.9562 16.359238260 -155.2822237 188.00070 -246.143725 278.86220
## 2005.9589 8.315842121 -163.4447922 180.07648 -254.369380 271.00106
## 2005.9616 11.913976055 -159.9657479 183.79370 -250.953378 274.78133
## 2005.9644 17.207938518 -154.7907926 189.20667 -245.841421 280.25730
## 2005.9671 15.218028182 -156.8996279 187.33568 -248.013211 278.44927
## 2005.9699 2.446018792 -169.7904801 174.68252 -260.966975 265.85901
## 2005.9726 6.112418176 -166.2428416 178.46768 -257.482205 269.70704
## 2005.9753 5.659208178 -166.8147306 178.13315 -258.116919 269.43534
## 2005.9781 3.537272747 -169.0552635 176.12981 -260.420233 267.49478
## 2005.9808 10.089589069 -162.6214633 182.80064 -254.049172 274.22835
## 2005.9836 12.231175991 -160.5983111 185.06066 -252.088715 276.55107
## 2005.9863 16.863428571 -156.0844122 189.81127 -247.637469 281.36433
## 2005.9890 15.401866603 -157.6642469 188.46798 -249.279913 280.08365
## 2005.9918 -1.723815351 -174.9081208 171.46049 -266.586354 263.13872
## 2005.9945 11.778424288 -161.5239925 185.08084 -253.264750 276.82160
## 2005.9973 13.395149732 -160.0252980 186.81560 -251.828538 278.61884
## 2006.0000 11.403125811 -162.1352725 184.94152 -254.000951 276.80720
## 2006.0027 32.225373152 -141.4308957 205.88164 -233.358971 297.80972
## 2006.0055 16.897052145 -156.8770072 190.67111 -248.867438 282.66154##NOTE: AIC = 28718.12 , BIC = 28735.20 , RMSE = 14.87674
Also, the headline of the plot below contains ETS(A,N,N) showing that the automated model characterized error of the “tsWSR_PK” SERIES as Additative (A), trend as None (A) and seasonality as None (N) which is equivalent to simple exponential model(ses) with only alpha parameter i.e level.
#Model 2 : ARIMA Models(AutoRegressive Moving Average) It is used for forecasting for both seasonal and non- seasonal level.
#Changing to stationary set
train.sta_Var8 <- diff(train7)
test.sta_Var8 <- diff(test7)#2.1 Auto Arima model without sesonality:
set.seed(301)
model_Var8 <- auto.arima(train.sta_Var8, seasonal = FALSE)
summary(model_Var8)## Series: train.sta_Var8
## ARIMA(2,0,3) with zero mean
##
## Coefficients:
## ar1 ar2 ma1 ma2 ma3
## -0.7108 0.2034 0.2693 -0.8819 -0.2156
## s.e. 0.0735 0.0493 0.0732 0.0211 0.0521
##
## sigma^2 estimated as 236.6: log likelihood=-9099.49
## AIC=18210.98 AICc=18211.02 BIC=18245.14
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 0.004778148 15.36312 11.41507 Inf Inf 0.6234888 0.001061865NOTE: AIC = 18210.98 , BIC = 18245.14 , RMSE = 15.36312
tsdisplay(residuals(model_Var8), lag.max = 45, main = '(1,1,1) Model Residuals')
#2.2 Auto Arima model with sesonality:
set.seed(301)
model2_Var8 <- auto.arima(train.sta_Var8, seasonal= TRUE)
summary(model2_Var8)## Series: train.sta_Var8
## ARIMA(2,0,3) with zero mean
##
## Coefficients:
## ar1 ar2 ma1 ma2 ma3
## -0.7108 0.2034 0.2693 -0.8819 -0.2156
## s.e. 0.0735 0.0493 0.0732 0.0211 0.0521
##
## sigma^2 estimated as 236.6: log likelihood=-9099.49
## AIC=18210.98 AICc=18211.02 BIC=18245.14
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 0.004778148 15.36312 11.41507 Inf Inf 0.6234888 0.001061865##NOTE: AIC = 18210.98 , BIC = 18245.14 , RMSE = 15.36312
tsdisplay(residuals(model2_Var8), lag.max = 20, main = 'Seasonal Model Residuals')
NOTE: Above Graphs shows serious lags at 13
#2.3 Manual Arima Passing parameter order = (2,0,13) which means p(member of lags of a variable to be used as a predictor) = 1, d = 0(members of differences needed for stationarity) and q = 18 (moving average order - number of lagged forecasts error in the prediction equation)
set.seed(301)
model1_Var8 <- arima(train.sta_Var8, order = c(2,0,13))
summary(model1_Var8)##
## Call:
## arima(x = train.sta_Var8, order = c(2, 0, 13))
##
## Coefficients:
## ar1 ar2 ma1 ma2 ma3 ma4 ma5 ma6
## -0.0318 -0.3921 -0.4083 0.0161 -0.2453 -0.1824 0.0020 -0.0359
## s.e. 0.3417 0.2325 0.3409 0.2702 0.1662 0.0909 0.0306 0.0293
## ma7 ma8 ma9 ma10 ma11 ma12 ma13 intercept
## 0.022 -0.0494 0.0428 -0.0130 0.0206 -0.0491 0.0575 -0.0002
## s.e. 0.027 0.0255 0.0269 0.0302 0.0262 0.0247 0.0238 0.0410
##
## sigma^2 estimated as 234.8: log likelihood = -9093.8, aic = 18221.59
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 0.01190884 15.32315 11.36616 Inf Inf 0.590761 -8.850224e-05##NOTE: AIC = 18221.59 , RMSE = 15.32315
tsdisplay(residuals(model1_Var8), lag.max = 20, main = 'Seasonal Model Residuals')
Note: It seems good fit.
Fit the observed with the predicted values for both models in the same plot.
par(mfrow = c(2,2))
fit_auto_train_Var8 %>% forecast(h=341) %>% autoplot() 
model1_Var8 %>% forecast(h=341) %>% autoplot() 
model2_Var8 %>% forecast(h=341) %>% autoplot() 
model_Var8 %>% forecast(h=341) %>% autoplot()
COMMENT:
1. The plots includes 80% to 95% confidence interval.
2. For ARIMA models it plots the forecast but because of the nature of autoregressive process of 2 lags, these forecast stabilizes quite smoothly.
Plot and comment on the residuals of the fitted data for both models in the same plot.
Residual Plot - to confirm no problem with this model
par(mfrow= c(2,2))
hist(fit_auto_train_Var8$residuals,col = 'red',xlab = 'Error',main = 'Histogram Of Residuals',freq= FALSE)
lines(density(fit_auto_train_Var8$residuals))
hist(model_Var8$residuals,col = 'red',xlab = 'Error',main = 'Histogram Of Residuals',freq= FALSE)
lines(density(model_Var8$residuals))
hist(model1_Var8$residuals,col = 'red',xlab = 'Error',main = 'Histogram Of Residuals',freq= FALSE)
lines(density(model1_Var8$residuals))
hist(model2_Var8$residuals,col = 'red',xlab = 'Error',main = 'Histogram Of Residuals',freq= FALSE)
lines(density(model2_Var8$residuals))
OBSERVATION: The residuals for each model are normally distributed, which shows the good fit of the models. It is normally distrbuted.
Testing the autocorrelation and partial autocorrelation of the residuals (using the plots and Ljung-Box Q statistic) up to an appropriate lag *
- ACF & PACF Plots
par(mfrow = c(4,2))
acf(fit_auto_train_Var8$residuals, main = 'Correlogram')
pacf(fit_auto_train_Var8$residuals, main = 'Partial Corelogram')
acf(model_Var8$residuals, main = 'Correlogram')
pacf(model_Var8$residuals, main = 'Partial Corelogram')
acf(model1_Var8$residuals, main = 'Correlogram')
pacf(model1_Var8$residuals, main = 'Partial Corelogram')
acf(model2_Var8$residuals, main = 'Correlogram')
pacf(model2_Var8$residuals, main = 'Partial Corelogram')
NOTE:
1. Residuals are the difference between actaual and fitted values
2. These blue lines are signficance bounds
3. This graph shows us the autocorelations for insample forecast errors
4. Do not exceed these significance bounds for lags 1 to end
- Ljunx-Box Test to check the autocorelations of the residuals
HO: No serial correlation upto 20 lags (does not exhibit lack of fit of the model)
Ha: Serial corelation is present (the model exhibits lack of fit)
We reject the null hypothesis, if p value is less than 0.05. This test is generally done for ARIMA models
Box.test(model_Var8$residuals, lag =20, type = 'Ljung-Box')##
## Box-Ljung test
##
## data: model_Var8$residuals
## X-squared = 27.528, df = 20, p-value = 0.1211Box.test(model1_Var8$residuals, lag =20, type = 'Ljung-Box')##
## Box-Ljung test
##
## data: model1_Var8$residuals
## X-squared = 9.6952, df = 20, p-value = 0.9734Box.test(model2_Var8$residuals, lag =20, type = 'Ljung-Box')##
## Box-Ljung test
##
## data: model2_Var8$residuals
## X-squared = 27.528, df = 20, p-value = 0.1211OBSERVATIONS: For above performed Ljunx-Box Test on ARIMA models output, we can say that p-value is more than significance level 0.05, then there is not a statistical significance.
We conclude that there is a liitle evidence of non-zero auto-corelations in the insample forecast errors at lags 1 to 20.
So we fail to rejects the null hypothesis. Hence, we conclude that there is no serial auto corelation present between lags. Hence, the model seems to be good fit.
par(mfrow = c(2,2))
qqnorm(fit_auto_train_Var8$residuals)
qqnorm(model_Var8$residuals)
qqnorm(model1_Var8$residuals)
qqnorm(model2_Var8$residuals)
Validating The Model by testing the model performance with Holdout set
Here, choosing RMSE as evaluation parameter. The lower RMSE indicates a more accurate forecast.
Below, is the comparison of model. We are fitting the model to test set which is the holdout set. And checking the accuracy using RMSE(Root mean square error) evaluation parameter.
accuracy(forecast(fit_auto_train_Var8), test7) ["Test set", "RMSE"]## [1] 22.98142#o/p - 22.98142accuracy(forecast(model1_Var8), test.sta_Var8) ["Test set", "RMSE"]## [1] 16.92509#O/P - 16.92509accuracy(forecast(model2_Var8), test.sta_Var8) ["Test set", "RMSE"]## [1] 16.9194#o/p - 16.9194accuracy(forecast(model_Var8), test.sta_Var8) ["Test set", "RMSE"]## [1] 16.9194#O/P - 16.9194NOTE:- Here, the RMSE value is less of ARIMA models compared to exponential model.
The minimum RMSE is of model2_Var8
COMMENT ON BEST MODEL AND ITS PARAMETERS
We observed the best model to be ARIMA model i.e.“model2_Var8”.
summary(model2_Var8)## Series: train.sta_Var8
## ARIMA(2,0,3) with zero mean
##
## Coefficients:
## ar1 ar2 ma1 ma2 ma3
## -0.7108 0.2034 0.2693 -0.8819 -0.2156
## s.e. 0.0735 0.0493 0.0732 0.0211 0.0521
##
## sigma^2 estimated as 236.6: log likelihood=-9099.49
## AIC=18210.98 AICc=18211.02 BIC=18245.14
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 0.004778148 15.36312 11.41507 Inf Inf 0.6234888 0.001061865Best model is ARIMA(2,0,3) ,which means
p = 2 d = 0 q = 3
For the best model, 2 member of lag is used as a predictor. As we transformed the series to stationary so members of differences needed for stationarity is 0. 3 are the number of lagged forecasts errors used in the prediction equation.
AIC = 18210.98, RMSE = 15.36312 which is minimum as compared to other models.
9. Forecasting on T-Totals
#Checking the attributes of time series
attributes(tsTT)## $tsp
## [1] 1998.00 2004.94 365.00
##
## $class
## [1] "ts"#Plotting the series
plot(tsTT, main = " T-Totals ", col = "red")
From the plot, we observes that there seems to have no trend but seems to have seasonlity.
Checking the statistics and visualising the missing data in the series:
plotNA.distribution(tsTT)
As data is missing at random. Hence, using na_locf method to impute the missing data.
#Impute the missing values with “na_locf” function of “imputeTS package” and visualise the imputed values in the time series
tsTT.imp <- na_locf(tsTT)
plotNA.imputations(tsTT, tsTT.imp)
#Decomposition Of Time Series
decomp8 <- decompose(tsTT.imp)
plot(decomp8, col = "red")
OBSERVATIONS:
1)There seems to have trend.
2)We observes the upward trend from year 2000 to 2003 and then further downward trend till 2004.
3)We observe some seasonality in the series. Seasonality describes cyclical effects due to the time of the year.
Let’s explore this seasonality pattern by plotting the decomp$seasonal components such that y-axis represents Seasonality Index and x-axis has month.
plot(decomp8$seasonal[1:365], type ='b', xlab = 'Years', ylab = 'Seasonality Index', col = 'blue', las = 2, main = "SEASONAL DATA")
OBSERVATIONS:
1) There is increase in TT for mid month of the year
2) There is a huge drop of TT for starting and end months of the year.
Stationarity check of time series
We could check the stationarity of time series by ADF and KPSS Tests:
- Augmented Dickey- Fuller(ADF) t-statistic test for unit root
- Kwiatkowski-Phillips-Schmidt-Shin (KPSS) for level or trend stationarity
adf.test(tsTT.imp)## Warning in adf.test(tsTT.imp): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: tsTT.imp
## Dickey-Fuller = -6.9802, Lag order = 13, p-value = 0.01
## alternative hypothesis: stationary#P-value is smaller so it is stationary.
kpss.test(tsTT.imp, null="Trend")##
## KPSS Test for Trend Stationarity
##
## data: tsTT.imp
## KPSS Trend = 0.12999, Truncation lag parameter = 8, p-value = 0.07966#P-value is greater than 0.05, which shows trend statationary.
Second, we can check each for characteristics of stationarity by looking at the autocorrelation functions (ACF) of each signal. For a stationary signal, because we expect no dependence with time, we would expect the ACF to go to 0 for each time lag (τ). Lets visualize the signals and ACFs.
acf(tsTT.imp,lag.max = length(tsTT.imp),xlab = "lag #", ylab = 'ACF',main='Statiionary Check ')
Here, we observes most of the data lies outside the blue-dotted lines means the significance level.
Now, we will take the difference to make our data stationary.
It seems difference of 1 is sufficient to make the series stationary.
tsTT.sta <- diff(tsTT.imp)
acf(tsTT.sta, lag.max = length(tsTT.sta),xlab = "lag #", ylab = 'ACF',main='Statiionary Check ')
Hence, after differencing our series is now transformed to stationary time series.
#CREATING MODELS AND FORECASTING: USING EXPONENTIAL SMOOTHING AND ARIMA TECHNIQUES FOR TIME SERIES FORECASTING
1.Train - Test Split of the data
train8 <- window(tsTT.imp, end = c(2004, 3))
test8 <- window(tsTT.imp, start = c(2004, 4))#Model 1 : Auto Exponential Smoothening Model
set.seed(301)
fit_auto_train_Var9 <- forecast(train8)
summary(fit_auto_train_Var9)##
## Forecast method: STL + ETS(A,N,N)
##
## Model Information:
## ETS(A,N,N)
##
## Call:
## ets(y = na.interp(x), model = etsmodel, allow.multiplicative.trend = allow.multiplicative.trend)
##
## Smoothing parameters:
## alpha = 0.1081
##
## Initial states:
## l = 41.5637
##
## sigma: 8.9365
##
## AIC AICc BIC
## 26480.80 26480.81 26497.88
##
## Error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 0.003227413 8.932469 6.564425 -Inf Inf 0.6349621 0.3549989
##
## Forecasts:
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 2004.0082 38.05206 26.599417775 49.50470 20.536754953 55.56737
## 2004.0110 44.13985 32.620459208 55.65923 26.522464120 61.75723
## 2004.0137 43.71898 32.133232347 55.30473 26.000108537 61.43785
## 2004.0164 45.50479 33.853056831 57.15651 27.685004362 63.32457
## 2004.0192 31.34877 19.631431669 43.06611 13.428647226 49.26889
## 2004.0219 35.67864 23.896057690 47.46122 17.658734672 53.69855
## 2004.0247 44.40569 32.558224073 56.25316 26.286552683 62.52483
## 2004.0274 33.64943 21.737433140 45.56144 15.431600475 51.86727
## 2004.0301 43.38445 31.408262045 55.36063 25.068452175 61.70044
## 2004.0329 37.24568 25.205647338 49.28570 18.832041391 55.65931
## 2004.0356 29.63456 17.531030310 41.73810 11.123806546 48.14532
## 2004.0384 40.10417 27.937462816 52.27088 21.496796706 58.71154
## 2004.0411 45.43561 33.206056083 57.66517 26.732120377 64.13910
## 2004.0438 45.14160 32.849515531 57.43368 26.342480330 63.94071
## 2004.0466 30.50848 18.154191007 42.86278 11.614223828 49.40274
## 2004.0493 41.67156 29.255369553 54.08775 22.682635397 60.66048
## 2004.0521 36.67938 24.201599640 49.15716 17.596261051 55.76250
## 2004.0548 27.72467 15.185602976 40.26374 8.547820103 46.90153
## 2004.0575 29.70543 17.105365870 42.30549 10.435296526 48.97556
## 2004.0603 36.68991 24.029155249 49.35067 17.326954966 56.05287
## 2004.0630 31.46150 18.740331913 44.18266 12.006153996 50.91684
## 2004.0658 40.85418 28.072891495 53.63546 21.306887076 60.40147
## 2004.0685 39.19012 26.348994611 52.03125 19.551312698 58.82893
## 2004.0712 36.89381 23.993124903 49.79450 17.163912432 56.62372
## 2004.0740 33.53295 20.572969702 46.49293 13.712371582 53.35352
## 2004.0767 37.58838 24.569383057 50.60738 17.677542218 57.49922
## 2004.0795 44.89515 31.817396862 57.97290 24.894454299 64.89584
## 2004.0822 47.73714 34.600895642 60.87337 27.646990457 67.82728
## 2004.0849 40.45803 27.263562801 53.65250 20.278832248 60.63723
## 2004.0877 40.58408 27.331632291 53.83652 20.316211812 60.85194
## 2004.0904 43.20534 29.895169910 56.51550 22.849193180 63.56148
## 2004.0932 47.38589 34.018252483 60.75353 26.941851444 67.82993
## 2004.0959 39.10380 25.678933871 52.52867 18.572238771 59.63536
## 2004.0986 35.42049 21.938637309 48.90234 14.801776736 56.03920
## 2004.1014 35.44482 21.906223542 48.98341 14.739324462 56.15031
## 2004.1041 38.81612 25.221019801 52.41122 18.024207589 59.60804
## 2004.1068 41.03925 27.387870372 54.69062 20.161268847 61.91722
## 2004.1096 43.53861 29.831194818 57.24603 22.574926274 64.50230
## 2004.1123 42.82059 29.057355513 56.58382 21.771540749 63.86963
## 2004.1151 40.62689 26.808070445 54.44571 19.492828798 61.76095
## 2004.1178 45.29577 31.421580820 59.16995 24.077030191 66.51450
## 2004.1205 44.76894 30.839608400 58.69827 23.465865285 66.07202
## 2004.1233 25.56919 11.584929658 39.55345 4.182109175 46.95627
## 2004.1260 29.75068 15.711706585 43.78966 8.279922499 51.22144
## 2004.1288 43.71397 29.620494686 57.80745 22.159859439 65.26808
## 2004.1315 45.04934 30.901569266 59.19710 23.412194000 66.68648
## 2004.1342 42.04024 27.838394020 56.24209 20.320388602 63.76010
## 2004.1370 33.65704 19.401308994 47.91277 11.854782042 55.45929
## 2004.1397 36.61034 22.300937982 50.91975 14.725996885 58.49469
## 2004.1425 40.82219 26.459308578 55.18507 18.856059522 62.78832
## 2004.1452 47.26170 32.845539452 61.67785 25.214087441 69.30930
## 2004.1479 44.71297 30.243733078 59.18221 22.584181956 66.84176
## 2004.1507 49.21724 34.695114434 63.73936 27.007566907 71.42691
## 2004.1534 43.63344 29.058621168 58.20826 21.343178824 65.92370
## 2004.1562 40.03627 25.408943803 54.66359 17.665707132 62.40682
## 2004.1589 44.96472 30.285077589 59.64436 22.514146002 67.41529
## 2004.1616 37.45906 22.727289795 52.19083 14.928761644 59.98936
## 2004.1644 38.03190 23.248183129 52.81562 15.422155726 60.64165
## 2004.1671 47.28856 32.453076082 62.12404 24.599645717 69.97747
## 2004.1699 45.43330 30.546231724 60.32037 22.665493683 68.20111
## 2004.1726 47.98295 33.044472988 62.92142 25.136521567 70.82938
## 2004.1753 48.06944 33.079736897 63.05915 25.144665426 70.99422
## 2004.1781 44.71185 29.671082826 59.75261 21.708983679 67.71471
## 2004.1808 46.31142 31.219774009 61.40307 23.230738621 69.39210
## 2004.1836 33.95589 18.813532667 49.09825 10.797651554 57.11413
## 2004.1863 35.10157 19.908662164 50.29447 11.866024936 58.33711
## 2004.1890 35.40598 20.162705601 50.64926 12.093400974 58.71857
## 2004.1918 33.34715 18.053665295 48.64064 9.957781108 56.73653
## 2004.1945 43.19716 27.853621061 58.54069 19.731244294 66.66307
## 2004.1973 47.63298 32.239560023 63.02640 24.090776805 71.17518
## 2004.2000 44.74159 29.298450862 60.18473 21.123346488 68.35983
## 2004.2027 48.03858 32.545875147 63.53128 24.344534091 71.73262
## 2004.2055 52.22363 36.681522793 67.76574 28.454028722 75.99323
## 2004.2082 49.88108 34.289723037 65.47243 26.036158820 73.72600
## 2004.2110 46.61843 30.977984539 62.25888 22.698432264 70.53843
## 2004.2137 43.18428 27.494890145 58.87366 19.189431130 67.17912
## 2004.2164 36.38216 20.643991218 52.12034 12.312706020 60.45162
## 2004.2192 41.22820 25.441388862 57.01501 17.084357294 65.37204
## 2004.2219 46.48482 30.649522366 62.32011 22.266823504 70.70281
## 2004.2247 46.27708 30.393447445 62.16071 21.985159641 70.56900
## 2004.2274 43.85501 27.923180462 59.78683 19.489381354 68.22063
## 2004.2301 40.99337 25.013501296 56.97325 16.554267822 65.43248
## 2004.2329 43.45054 27.422765133 59.47832 18.938173537 67.96291
## 2004.2356 43.16291 27.087378908 59.23845 18.577504752 67.74832
## 2004.2384 40.15470 24.031547594 56.27785 15.496465771 64.81294
## 2004.2411 47.49680 31.326171648 63.66743 22.765956387 72.22765
## 2004.2438 50.90476 34.686793247 67.12273 26.101518126 75.70801
## 2004.2466 53.31754 37.052366886 69.58271 28.442104841 78.19297
## 2004.2493 51.21627 34.904033500 67.52851 26.268856833 76.16368
## 2004.2521 45.32464 28.965474270 61.68381 20.305454659 70.34383
## 2004.2548 48.02115 31.615186172 64.42711 22.930394681 73.11190
## 2004.2575 45.30211 28.849488798 61.75474 20.139995884 70.46423
## 2004.2603 37.18714 20.687983307 53.68629 11.953858828 62.42042
## 2004.2630 41.42110 24.875547379 57.96665 16.116860605 66.72534
## 2004.2658 40.70115 24.109322741 57.29297 15.326142361 66.07615
## 2004.2685 45.73603 29.098065876 62.37399 20.290460006 71.18160
## 2004.2712 40.05556 23.371586613 56.73954 14.539622802 65.57150
## 2004.2740 41.39062 24.660752854 58.12048 15.804498095 66.97673
## 2004.2767 42.69612 25.920495519 59.47174 17.040016256 68.35222
## 2004.2795 37.77019 20.948929844 54.59145 12.044291978 63.49609
## 2004.2822 45.87669 29.009911098 62.74346 20.081179995 71.67219
## 2004.2849 47.48571 30.573547618 64.39788 21.620788117 73.35064
## 2004.2877 49.01629 32.058851095 65.97372 23.082127513 74.95044
## 2004.2904 44.38267 27.380084469 61.38525 18.379460610 70.38587
## 2004.2932 46.88631 29.838699255 63.93392 20.814238415 72.95838
## 2004.2959 44.40388 27.311359304 61.49640 18.263124281 70.54464
## 2004.2986 49.12578 31.988462571 66.26309 22.916515667 75.33504
## 2004.3014 52.08333 34.901342722 69.26533 25.805745754 78.36092
## 2004.3041 49.44831 32.221753311 66.67486 23.102567613 75.79404
## 2004.3068 48.44035 31.169355041 65.71135 22.026641473 74.85406
## 2004.3096 45.52237 28.207037607 62.83769 19.040856561 72.00387
## 2004.3123 49.53341 32.173860103 66.89295 22.984271508 76.08254
## 2004.3151 46.13875 28.735096005 63.54240 19.522159332 72.75534
## 2004.3178 47.07126 29.623615919 64.51891 20.387390190 73.75513
## 2004.3205 47.05234 29.560810141 64.54387 20.301353931 73.80332
## 2004.3233 47.02329 29.487984021 64.55859 20.205355466 73.84122
## 2004.3260 50.02484 32.445873941 67.60381 23.140130743 76.90955
## 2004.3288 51.98681 34.364285948 69.60933 25.035485378 78.93813
## 2004.3315 44.28756 26.621589108 61.95353 17.269788016 71.30534
## 2004.3342 37.22445 19.515135599 54.93377 10.140390417 64.30851
## 2004.3370 46.14720 28.394643350 63.89975 18.997010094 73.29738
## 2004.3397 49.93302 32.137336599 67.72870 22.716870877 77.14917
## 2004.3425 46.54110 28.702390668 64.37981 19.259147687 73.82305
## 2004.3452 41.28752 23.405885509 59.16915 13.939920076 68.63512
## 2004.3479 40.25724 22.332779925 58.18169 12.844146453 67.67032
## 2004.3507 44.70684 26.739668001 62.67402 17.228420514 72.18526
## 2004.3534 48.49030 30.480506707 66.50009 20.946698845 76.03390
## 2004.3562 44.13151 26.079199763 62.18382 16.522884787 71.74013
## 2004.3589 40.69984 22.605109922 58.79456 13.026340715 68.37333
## 2004.3616 52.27126 34.134212016 70.40830 24.533041093 80.00947
## 2004.3644 48.30986 30.130600146 66.48913 20.507079652 76.11265
## 2004.3671 47.92910 29.707719067 66.15049 20.061900788 75.79631
## 2004.3699 48.03246 29.769049880 66.29587 20.100985241 75.96393
## 2004.3726 46.66880 28.363463646 64.97414 18.673203719 74.66440
## 2004.3753 49.59329 31.246121281 67.94046 21.533716788 77.65286
## 2004.3781 50.46473 32.075825671 68.85364 22.341326988 78.58814
## 2004.3808 47.55460 29.124056689 65.98515 19.367513848 75.74170
## 2004.3836 45.22935 26.757253685 63.70145 16.978716382 73.47998
## 2004.3863 50.87390 32.360347107 69.38745 22.559864702 79.18793
## 2004.3890 50.85345 32.298538161 69.40837 22.476159683 79.23075
## 2004.3918 46.97410 28.377914444 65.57029 18.533688596 75.41451
## 2004.3945 47.51414 28.876774538 66.15150 19.010749699 76.01753
## 2004.3973 49.13797 30.459518558 67.81642 20.571742786 77.70420
## 2004.4000 50.62915 31.909703603 69.34861 22.000224641 79.25809
## 2004.4027 50.39761 31.637247345 69.15797 21.706112621 79.08910
## 2004.4055 48.81289 30.011714536 67.61407 20.058971172 77.56682
## 2004.4082 48.64098 29.799064778 67.48289 19.824759586 77.45719
## 2004.4110 48.05093 29.168379804 66.93349 19.172559295 76.92931
## 2004.4137 44.79901 25.875902110 63.72212 15.858612495 73.73941
## 2004.4164 44.52847 25.564891744 63.49205 15.526178937 73.53076
## 2004.4192 48.34381 29.339845905 67.34777 19.279755528 77.40786
## 2004.4219 48.11349 29.069232301 67.15775 18.987809683 77.23918
## 2004.4247 52.62444 33.539962668 71.70891 23.437252854 81.81162
## 2004.4274 51.26988 32.145279165 70.39448 22.021326915 80.51843
## 2004.4301 49.88853 30.723885070 69.05317 20.578734862 79.19833
## 2004.4329 47.79433 28.589726158 66.99894 18.423422192 77.16524
## 2004.4356 47.74031 28.495825722 66.98479 18.308411922 77.17221
## 2004.4384 47.84330 28.559025647 67.12758 18.350545667 77.33606
## 2004.4411 48.48126 29.157270872 67.80525 18.927768093 78.03476
## 2004.4438 46.74444 27.380815639 66.10806 17.130333178 76.35854
## 2004.4466 48.21585 28.812676391 67.61902 18.541257100 77.89044
## 2004.4493 50.18783 30.745191913 69.63048 20.452878380 79.92279
## 2004.4521 50.50706 31.025026590 69.98909 20.711861148 80.30226
## 2004.4548 49.80402 30.282674128 69.32536 19.948698852 79.65934
## 2004.4575 49.42998 29.869405932 68.99056 19.514662642 79.34530
## 2004.4603 48.88649 29.286762356 68.48622 18.911292622 78.86169
## 2004.4630 48.21846 28.579652011 67.85726 18.183497155 78.25341
## 2004.4658 48.20442 28.526616053 67.88222 18.109817151 78.29902
## 2004.4685 50.44060 30.723878480 70.15732 20.286476363 80.59472
## 2004.4712 51.12620 31.370629630 70.88176 20.912664888 81.33973
## 2004.4740 48.68358 28.889251569 68.47792 18.410764554 78.95640
## 2004.4767 49.86503 30.032006076 69.69806 19.533036902 80.19702
## 2004.4795 48.78316 28.911517949 68.65480 18.392106496 79.17421
## 2004.4822 47.71027 27.800091067 67.62046 17.260276985 78.16027
## 2004.4849 48.95910 29.010448013 68.90775 18.450270719 79.46792
## 2004.4877 50.28805 30.301004347 70.27509 19.720503033 80.85559
## 2004.4904 47.14507 27.119704561 67.17043 16.518918192 77.77122
## 2004.4932 45.37714 25.313536307 65.44075 14.692503625 76.06179
## 2004.4959 48.13629 28.034503916 68.23807 17.393263442 78.87931
## 2004.4986 49.50418 29.364295822 69.64406 18.702885858 80.30547
## 2004.5014 48.08339 27.905480557 68.26130 17.223939189 78.94285
## 2004.5041 47.07993 26.864056971 67.29580 16.162422069 77.99743
## 2004.5068 49.22253 28.968772260 69.47628 18.247081481 80.19798
## 2004.5096 48.86524 28.573668620 69.15681 17.831959411 79.89852
## 2004.5123 46.58730 26.257981449 66.91662 15.496291046 77.67831
## 2004.5151 49.91359 29.546597487 70.28058 18.764962921 81.06222
## 2004.5178 50.67173 30.267134239 71.07633 19.465592335 81.87787
## 2004.5205 51.13840 30.696260657 71.58053 19.874848037 82.40194
## 2004.5233 50.76686 30.287258715 71.24646 19.446011799 82.08771
## 2004.5260 49.18333 28.666330191 69.70033 17.805285202 80.56138
## 2004.5288 48.84676 28.292423184 69.40109 17.411616144 80.28190
## 2004.5315 49.37314 28.781537937 69.96473 17.881004673 80.86527
## 2004.5342 50.24134 29.612545583 70.87013 18.692321729 81.79036
## 2004.5370 49.48282 28.816892451 70.14874 17.877013448 81.08862
## 2004.5397 49.21796 28.514978298 69.92095 17.555479396 80.88045
## 2004.5425 49.54475 28.804771406 70.28474 17.825687666 81.26382
## 2004.5452 47.80338 27.026463204 68.58029 16.027829499 79.57892
## 2004.5479 49.97938 29.165602550 70.79316 18.147453569 81.81131
## 2004.5507 48.53662 27.686045930 69.38720 16.648416178 80.42483
## 2004.5534 48.28804 27.400727795 69.17536 16.343651594 80.23243
## 2004.5562 47.18766 26.263671904 68.11164 15.187183394 79.18813
## 2004.5589 49.47571 28.515116351 70.43630 17.419249495 81.53217
## 2004.5616 48.23248 27.235346919 69.22962 16.120135501 80.34483
## 2004.5644 46.39473 25.361115438 67.42834 14.226593065 78.56286
## 2004.5671 48.77722 27.707185728 69.84724 16.553385836 81.00104
## 2004.5699 49.73392 28.627534742 70.84030 17.454490589 82.01334
## 2004.5726 49.91538 28.772710990 71.05806 17.580455667 82.25031
## 2004.5753 50.09602 28.917116651 71.27492 17.705683076 82.48635
## 2004.5781 51.36684 30.151774458 72.58191 18.921195382 83.81249
## 2004.5808 48.15113 26.899953988 69.40230 15.650261993 80.65199
## 2004.5836 49.29017 28.002952421 70.57739 16.734179925 81.84616
## 2004.5863 49.63898 28.315783255 70.96219 17.027962510 82.25001
## 2004.5890 45.87819 24.519066317 67.23731 13.212229415 78.54415
## 2004.5918 49.47633 28.081346587 70.87132 16.755525454 82.19714
## 2004.5945 47.87939 26.448600746 69.31018 15.103827152 80.65495
## 2004.5973 49.86734 28.400807435 71.33387 17.037112987 82.69756
## 2004.6000 51.28499 29.782774918 72.78720 18.400191069 84.16978
## 2004.6027 49.79736 28.259526007 71.33520 16.858084051 82.73664
## 2004.6055 46.90040 25.327003321 68.47381 13.906734399 79.89408
## 2004.6082 48.17280 26.563894992 69.78171 15.124830090 81.22078
## 2004.6110 46.08592 24.441560466 67.73027 12.983730417 79.18810
## 2004.6137 48.61488 26.935135098 70.29463 15.458570585 81.77119
## 2004.6164 49.04702 27.331939699 70.76210 15.836671254 82.25737
## 2004.6192 49.24238 27.492029952 70.99274 15.978087960 82.50668
## 2004.6219 41.76949 19.983918580 63.55506 8.451333277 75.08765
## 2004.6247 45.75414 23.933401596 67.57487 12.382203071 79.12607
## 2004.6274 47.11822 25.262378502 68.97405 13.692596700 80.54384
## 2004.6301 48.29373 26.402839530 70.18461 14.814504251 81.77295
## 2004.6329 50.64259 28.716709835 72.56847 17.109850737 84.17533
## 2004.6356 50.96636 29.005545044 72.92718 17.380191643 84.55253
## 2004.6384 49.48269 27.486990779 71.47838 15.843172449 83.12220
## 2004.6411 49.68256 27.652033121 71.71308 15.989779099 83.37533
## 2004.6438 47.63864 25.573346084 69.70393 13.892685467 81.38459
## 2004.6466 49.61110 27.511088344 71.71111 15.812050091 83.41015
## 2004.6493 48.50768 26.373006402 70.64235 14.655619337 82.35974
## 2004.6521 48.05292 25.883644445 70.22220 14.147937256 81.95791
## 2004.6548 49.13792 26.934089401 71.34175 15.180090643 83.09575
## 2004.6575 46.39750 24.159172477 68.63584 12.386910571 80.40810
## 2004.6603 42.72889 20.456112498 65.00167 8.665615733 76.79217
## 2004.6630 45.64738 23.340212991 67.95456 11.531509524 79.76326
## 2004.6658 48.49685 26.155338955 70.83836 14.328456815 82.66525
## 2004.6685 42.28204 19.906236115 64.65784 8.061203201 76.50287
## 2004.6712 44.41372 22.003685415 66.82376 10.140529498 78.68691
## 2004.6740 45.87790 23.433684335 68.32212 11.552433058 80.20337
## 2004.6767 38.69111 16.212756971 61.16945 4.313437852 73.06877
## 2004.6795 41.22192 18.709490515 63.73435 6.792130947 75.65171
## 2004.6822 43.88480 21.338339919 66.43125 9.402967169 78.36662
## 2004.6849 41.61278 19.032345773 64.19321 7.078986988 76.14657
## 2004.6877 38.35397 15.739610328 60.96833 3.768292529 72.93964
## 2004.6904 40.14876 17.500528136 62.79699 5.511278226 74.78624
## 2004.6932 38.95567 16.273610723 61.63772 4.266455480 73.64488
## 2004.6959 34.24959 11.533756997 56.96542 -0.491276915 68.99045
## 2004.6986 43.15792 20.408364038 65.90747 8.365477998 77.95036
## 2004.7014 36.08008 13.296852929 58.86331 1.236141185 70.92402
## 2004.7041 36.37878 13.561928004 59.19563 1.483416864 71.27414
## 2004.7068 38.61642 15.765990719 61.46684 3.669706374 73.56313
## 2004.7096 43.87718 20.993226186 66.76113 8.879194713 78.87516
## 2004.7123 41.47336 18.555933029 64.39079 6.424180389 76.52254
## 2004.7151 35.86079 12.909938576 58.81165 0.760490618 70.96109
## 2004.7178 34.91067 11.926435874 57.89490 -0.240681669 70.06202
## 2004.7205 38.20614 15.188572925 61.22370 3.003811423 73.40846
## 2004.7233 43.17130 20.120452169 66.22214 7.918072218 78.42452
## 2004.7260 46.49246 23.408384848 69.57654 11.188411851 81.79651
## 2004.7288 44.01490 20.897630321 67.13216 8.660089570 79.36970
## 2004.7315 35.38183 12.231428800 58.53224 -0.023654521 70.78732
## 2004.7342 41.16998 17.986484639 64.35347 5.713883822 76.62608
## 2004.7370 30.42040 7.203861315 53.63694 -5.086232028 65.92703
## 2004.7397 32.39939 9.149852258 55.64892 -3.157708751 67.95649
## 2004.7425 41.97294 18.690448772 65.25542 6.365444855 77.58043
## 2004.7452 43.17363 19.858240177 66.48902 7.515818002 78.83144
## 2004.7479 42.78089 19.432643709 66.12914 7.072827823 78.48896
## 2004.7507 40.05617 16.675115109 63.43723 4.297929956 75.81442
## 2004.7534 39.00978 15.595954439 62.42360 3.201424359 74.81813
## 2004.7562 44.20856 20.762015448 67.65510 8.350164680 80.06695
## 2004.7589 37.85204 14.372825528 61.33126 1.943678209 73.76041
## 2004.7616 39.70472 16.192870008 63.21656 3.746450175 75.66298
## 2004.7644 38.59131 15.046877901 62.13574 2.583209490 74.59941
## 2004.7671 35.28048 11.703515779 58.85745 -0.777377371 71.33835
## 2004.7699 28.16824 4.558773492 51.77770 -7.939320660 64.27579
## 2004.7726 40.15278 16.510867564 63.79469 3.995596053 76.30996
## 2004.7753 41.32734 17.653023898 65.00165 5.120598571 77.53408
## 2004.7781 34.82174 11.115065532 58.52842 -1.434490165 71.07797
## 2004.7808 39.17960 15.440613500 62.91860 2.873950786 75.48526
## 2004.7836 37.57790 13.806640410 61.34917 1.222893935 73.93291
## 2004.7863 36.22293 12.419435052 60.02642 -0.181372023 72.62722
## 2004.7890 28.20041 4.364739111 52.03609 -8.253105496 64.65394
## 2004.7918 25.77186 1.904047693 49.63968 -10.730811472 62.27454
## 2004.7945 30.20640 6.306489505 54.10632 -6.345361336 66.75817
## 2004.7973 35.98256 12.050591900 59.91453 -0.618227827 72.58335
## 2004.8000 39.63831 15.674329079 63.60229 2.988563163 76.28806
## 2004.8027 40.50417 16.508217635 64.50012 3.805528138 77.20281
## 2004.8055 37.55319 13.525312145 61.58107 0.805721584 74.30066
## 2004.8082 35.18123 11.121467988 59.24099 -1.615001210 71.97746
## 2004.8110 32.81643 8.724825729 56.90804 -4.028499768 69.66136
## 2004.8137 42.60917 18.485764083 66.73258 5.715604538 79.50273
## 2004.8164 37.40565 13.250483764 61.56081 0.463512333 74.34778
## 2004.8192 41.48322 17.296341012 65.67010 4.492579769 78.47386
## 2004.8219 29.39635 5.177792249 53.61490 -7.642736818 66.43543
## 2004.8247 36.66305 12.412857399 60.91324 -0.424417590 73.75051
## 2004.8274 37.14791 12.866125195 61.42969 0.012126100 74.28369
## 2004.8301 43.05347 18.740135754 67.36680 5.869434285 80.23750
## 2004.8329 40.39577 16.050928690 64.74062 3.163546493 77.62800
## 2004.8356 26.05467 1.678351812 50.43098 -11.225689550 63.33502
## 2004.8384 24.81776 0.410019116 49.22551 -12.510659933 62.14619
## 2004.8411 38.73874 14.299605112 63.17787 1.362309774 76.11517
## 2004.8438 44.05393 19.583451719 68.52441 6.629561406 81.47830
## 2004.8466 32.61054 8.108753291 57.11233 -4.861710765 70.08280
## 2004.8493 30.75888 6.225825108 55.29194 -6.761191540 68.27896
## 2004.8521 23.08254 -1.481747674 47.64683 -14.485295843 60.65037
## 2004.8548 31.22730 6.631822924 55.82278 -6.388235778 68.84283
## 2004.8575 32.26842 7.641791024 56.89504 -5.394757298 69.93159
## 2004.8603 40.64795 15.990215182 65.30569 2.937198069 78.35870
## 2004.8630 45.58187 20.893062320 70.27068 7.823597168 83.34014
## 2004.8658 34.01025 9.290409061 58.73009 -3.795483455 71.81598
## 2004.8685 34.26583 9.514993880 59.01666 -3.587305404 72.11896
## 2004.8712 32.74793 7.966143182 57.52972 -5.152542351 70.64840
## 2004.8740 34.63272 9.820021620 59.44543 -3.315029719 72.58048
## 2004.8767 42.42436 17.580776286 67.26794 4.429379505 80.41933
## 2004.8795 37.69305 12.818627636 62.56747 -0.349094296 75.73519
## 2004.8822 30.19451 5.289293120 55.09973 -7.894733748 68.28376
## 2004.8849 36.92234 11.986358091 61.85832 -1.213953573 75.05863
## 2004.8877 41.84988 16.883173658 66.81659 3.666597262 80.03316
## 2004.8904 39.62682 14.629423573 64.62421 1.396602438 77.85703
## 2004.8932 35.64712 10.619072328 60.67516 -2.629973630 73.92421
## 2004.8959 35.61822 10.559564233 60.67688 -2.705686702 73.94213
## 2004.8986 33.41806 8.328832132 58.50729 -4.952604009 71.78873
## 2004.9014 29.13459 4.014820345 54.25436 -9.282781301 67.55196
## 2004.9041 36.38628 11.236011959 61.53655 -2.077735565 74.85029
## 2004.9068 33.40616 8.225425138 58.58689 -5.104448707 71.91676
## 2004.9096 32.19031 6.979157111 57.40147 -6.366823569 70.74745
## 2004.9123 40.26730 15.025756823 65.50885 1.663688723 78.87092
## 2004.9151 47.97051 22.698605801 73.24241 9.320469627 86.62054
## 2004.9178 41.01660 15.714380797 66.31882 2.320195825 79.71300
## 2004.9205 34.66353 9.331034337 59.99603 -4.079180227 73.40625
## 2004.9233 37.60420 12.241455105 62.96694 -1.184769913 76.39317
## 2004.9260 29.73436 4.341412908 55.12732 -9.100803495 68.56953
## 2004.9288 28.05550 2.632376332 53.47862 -10.825812454 66.93681
## 2004.9315 33.36584 7.912584225 58.81911 -5.561558011 72.29325
## 2004.9342 19.47529 -6.008076007 44.95865 -19.498152826 58.44872
## 2004.9370 32.52023 7.006804036 58.03366 -6.499188567 71.53965
## 2004.9397 39.93585 14.392388262 65.47930 0.870498610 79.00119
## 2004.9425 36.81478 11.241326000 62.38823 -2.296442034 75.92600
## 2004.9452 34.62007 9.016657063 60.22348 -4.536970751 73.77711
## 2004.9479 33.51171 7.878368552 59.14504 -5.691100506 72.71451
## 2004.9507 36.17356 10.510336780 61.83679 -3.074955049 75.42208
## 2004.9534 31.48523 5.792143858 57.17831 -7.808952336 70.77940
## 2004.9562 34.96719 9.244283522 60.69009 -4.372598693 74.30697
## 2004.9589 29.21710 3.464416182 54.96979 -10.168233775 68.60244
## 2004.9616 32.79734 7.014903355 58.57978 -6.633496128 72.22818
## 2004.9644 36.00588 10.193726334 61.81804 -3.470404522 75.48217
## 2004.9671 35.89997 10.058124564 61.74181 -3.621719573 75.42165
## 2004.9699 30.40431 4.532817822 56.27580 -9.162721569 69.97134
## 2004.9726 29.42862 3.527511581 55.32972 -10.183705097 69.04094
## 2004.9753 32.24617 6.315479820 58.17685 -7.411396240 71.90373
## 2004.9781 33.39260 7.432367026 59.35283 -6.310150573 73.09535
## 2004.9808 32.23033 6.240578128 58.22007 -7.517563227 71.97821
## 2004.9836 36.43058 10.411354183 62.44981 -3.362393206 76.22356
## 2004.9863 36.94264 10.893960111 62.99131 -2.895375650 76.78065
## 2004.9890 33.79272 7.714631305 59.87081 -6.090275225 73.67572
## 2004.9918 24.27567 -1.831798247 50.38314 -15.652258003 64.20360
## 2004.9945 34.58791 8.451089014 60.72472 -5.384906486 74.56072
## 2004.9973 35.88607 9.719939499 62.05220 -4.131574320 75.90372
## 2005.0000 37.52110 11.325684208 63.71651 -2.541330563 77.58353
## 2005.0027 44.58918 18.364512872 70.81384 4.482014457 84.69634
## 2005.0055 34.13236 7.878484228 60.38625 -6.019480581 74.28421
## 2005.0082 38.05206 11.768995759 64.33513 -2.144418251 78.24854
## 2005.0110 44.13985 17.827629562 70.45206 3.898783487 84.38091
## 2005.0137 43.71898 17.377642835 70.06032 3.433381773 84.00458
## 2005.0164 45.50479 19.134361677 71.87521 5.174702650 85.83487
## 2005.0192 31.34877 4.949291377 57.74825 -9.025748650 71.72329
## 2005.0219 35.67864 9.250138864 62.10714 -4.740265253 76.09755
## 2005.0247 44.40569 17.948199246 70.86319 3.942447895 84.86894
## 2005.0274 33.64943 7.162980616 60.13589 -6.858101172 74.15697
## 2005.0301 43.38445 16.869065735 69.89983 2.832670254 83.93623
## 2005.0329 37.24568 10.701396610 63.78995 -3.350295874 77.84165
## 2005.0356 29.63456 3.061419845 56.20771 -11.005553009 70.27468
## 2005.0384 40.10417 13.502192464 66.70615 -0.580044179 80.78839
## 2005.0411 45.43561 18.804830730 72.06639 4.707346826 86.16388
## 2005.0438 45.14160 18.482044968 71.80115 4.369330274 85.91386
## 2005.0466 30.50848 3.820189801 57.19678 -10.307739262 71.32471
## 2005.0493 41.67156 14.954556931 68.38856 0.811429865 82.53169
## 2005.0521 36.67938 9.933699364 63.42506 -4.224609390 77.58337
## 2005.0548 27.72467 0.950343237 54.49900 -13.223130945 68.67248
## 2005.0575 29.70543 2.902479174 56.50837 -11.286144225 70.69700
## 2005.0603 36.68991 9.858378311 63.52145 -4.345378147 77.72520
## 2005.0630 31.46150 4.601405559 58.32159 -9.617467854 72.54046
## 2005.0658 40.85418 13.965560557 67.74280 -0.268413755 81.97677
## 2005.0685 39.19012 12.273007837 66.10723 -1.976051371 80.35629
## 2005.0712 36.89381 9.948234861 63.83939 -4.315893290 78.10352
## 2005.0740 33.53295 6.558932691 60.50696 -7.720248499 74.78614
## 2005.0767 37.58838 10.585959023 64.59080 -3.708259356 78.88502
## 2005.0795 44.89515 17.864349310 71.92594 3.555109545 86.23518
## 2005.0822 47.73714 20.677991558 74.79628 6.353746159 89.12052
## 2005.0849 40.45803 13.370572572 67.54549 -0.968662757 81.88473
## 2005.0877 40.58408 13.468329628 67.69982 -0.885879978 82.05403
## 2005.0904 43.20534 16.061331776 70.34934 1.692163498 84.71851
## 2005.0932 47.38589 20.213659019 74.55813 5.829547626 88.94224
## 2005.0959 39.10380 11.903368329 66.30423 -2.495670672 80.70327
## 2005.0986 35.42049 8.191885982 62.64909 -6.222065168 77.06304
## 2005.1014 35.44482 8.188075700 62.70156 -6.240772187 77.13041
## 2005.1041 38.81612 11.531267627 66.10098 -2.912461633 80.54471
## 2005.1068 41.03925 13.726308900 68.35218 -0.732286416 82.81078
## 2005.1096 43.53861 16.197621876 70.87960 1.724175773 85.35305
## 2005.1123 42.82059 15.451571659 70.18960 0.963289992 84.67788
## 2005.1151 40.62689 13.229878916 68.02390 -1.273223141 82.52700
## 2005.1178 45.29577 17.870787474 72.72075 3.352880157 87.23865
## 2005.1205 44.76894 17.316021664 72.22186 2.783324170 86.75456
## 2005.1233 25.56919 -1.911639525 53.05002 -16.459112159 67.59749
## 2005.1260 29.75068 2.241968363 57.25939 -12.320264419 71.82163
## 2005.1288 43.71397 16.177403253 71.25054 1.600425267 85.82752
## 2005.1315 45.04934 17.484942816 72.61373 2.893234528 87.20544
## 2005.1342 42.04024 14.448053072 69.63244 -0.158370665 84.23886
## 2005.1370 33.65704 6.037076343 61.27700 -8.584048031 75.89812
## 2005.1397 36.61034 8.962638657 64.25805 -5.673171589 78.89386
## 2005.1425 40.82219 13.146769798 68.49761 -1.503711598 83.14809
## 2005.1452 47.26170 19.558590585 74.96480 4.893452716 89.62994
## 2005.1479 44.71297 16.982205600 72.44373 2.302425891 87.12351
## 2005.1507 49.21724 21.458841889 76.97563 6.764434930 91.67004
## 2005.1534 43.63344 15.847439131 71.41944 1.138419467 86.12846
## 2005.1562 40.03627 12.222689841 67.84984 -2.500928025 82.57346
## 2005.1589 44.96472 17.123591223 72.80584 2.385389615 87.54404
## 2005.1616 37.45906 9.590412467 65.32771 -5.162358467 80.08048
## 2005.1644 38.03190 10.135758166 65.92804 -4.631567720 80.69537
## 2005.1671 47.28856 19.364948661 75.21217 4.583082155 89.99404
## 2005.1699 45.43330 17.482248840 73.38435 2.685856003 88.18074
## 2005.1726 47.98295 20.004483421 75.96141 5.193578500 90.77232
## 2005.1753 48.06944 20.063591181 76.07530 5.238188382 90.90070
## 2005.1781 44.71185 16.678633219 72.74506 1.838746705 87.58495
## 2005.1808 46.31142 18.250874459 74.37197 3.396518353 89.22632
## 2005.1836 33.95589 5.868038788 62.04375 -9.000772830 76.91256
## 2005.1863 35.10157 6.986431204 63.21670 -7.896821885 78.09995
## 2005.1890 35.40598 7.263596414 63.54837 -7.634084147 78.44605
## 2005.1918 33.34715 5.177538314 61.51677 -9.734555760 76.42886
## 2005.1945 43.19716 15.000338274 71.39397 0.073844605 86.32047
## 2005.1973 47.63298 19.408984942 75.85697 4.468105555 90.79785
## 2005.2000 44.74159 16.490448501 72.99273 1.535197235 87.94798
## 2005.2027 48.03858 19.760311996 76.31684 4.790702648 91.28645
## 2005.2055 52.22363 23.918266794 80.52899 8.934313123 95.51294
## 2005.2082 49.88108 21.548643559 78.21351 6.550359284 93.21179
## 2005.2110 46.61843 18.258952356 74.97791 3.246351156 89.99051
## 2005.2137 43.18428 14.797777413 71.57077 -0.229127071 86.59768
## 2005.2164 36.38216 7.968671452 64.79566 -7.072522714 79.83685
## 2005.2192 41.22820 12.787736915 69.66866 -2.267733371 84.72413
## 2005.2219 46.48482 18.017414408 74.95222 2.947681527 90.02195
## 2005.2247 46.27708 17.782760941 74.77140 2.698778950 89.85538
## 2005.2274 43.85501 15.333794151 72.37622 0.235576499 87.47444
## 2005.2301 40.99337 12.445295175 69.54145 -2.667144730 84.65389
## 2005.2329 43.45054 14.875620431 72.02546 -0.251028354 87.15211
## 2005.2356 43.16291 14.561178072 71.76465 -0.579666258 86.90549
## 2005.2384 40.15470 11.526174270 68.78323 -3.628852309 83.93825
## 2005.2411 47.49680 18.841510660 76.15210 3.672315090 91.32129
## 2005.2438 50.90476 22.222730580 79.58680 7.039379244 94.77015
## 2005.2466 53.31754 24.608789670 82.02629 9.411295752 97.22378
## 2005.2493 51.21627 22.480829992 79.95171 7.269206641 95.16333
## 2005.2521 45.32464 16.562533834 74.08675 1.336794162 89.31249
## 2005.2548 48.02115 19.232399267 76.80990 3.992556349 92.04974
## 2005.2575 45.30211 16.486746961 74.11748 1.232813837 89.37141
## 2005.2603 37.18714 8.345179134 66.02910 -6.922831193 81.29711
## 2005.2630 41.42110 12.552574511 70.28963 -2.729500051 85.57170
## 2005.2658 40.70115 11.806075852 69.59622 -3.490050014 84.89234
## 2005.2685 45.73603 16.814440654 74.65762 1.504276380 89.96778
## 2005.2712 40.05556 11.107479745 69.00365 -4.216710076 84.32784
## 2005.2740 41.39062 12.416062016 70.36517 -2.922140528 85.70337
## 2005.2767 42.69612 13.695119357 71.69712 -1.657083118 87.04932
## 2005.2795 37.77019 8.742767964 66.79761 -6.623421689 82.16380
## 2005.2822 45.87669 16.822864049 74.93051 1.442699940 90.31067
## 2005.2849 47.48571 18.405516882 76.56591 3.011391002 91.96003
## 2005.2877 49.01629 19.909739071 78.12283 4.501664072 93.53091
## 2005.2904 44.38267 15.249794463 73.51554 -0.172217039 88.93755
## 2005.2932 46.88631 17.727135465 76.04549 2.291200043 91.48142
## 2005.2959 44.40388 15.218426810 73.58934 -0.231419983 89.03918
## 2005.2986 49.12578 19.914067319 78.33749 4.450321669 93.80123
## 2005.3014 52.08333 22.845391519 81.32128 7.367759494 96.79891
## 2005.3041 49.44831 20.184153805 78.71246 4.692647852 94.20396
## 2005.3068 48.44035 19.150015716 77.73069 3.644648249 93.23606
## 2005.3096 45.52237 16.205867769 74.83886 0.686651170 90.35808
## 2005.3123 49.53341 20.190769870 78.87604 4.657716485 94.40910
## 2005.3151 46.13875 16.769996294 75.50750 1.223118439 91.05438
## 2005.3178 47.07126 17.676418438 76.46610 2.115728395 92.02679
## 2005.3205 47.05234 17.631427378 76.47325 2.056937395 92.04774
## 2005.3233 47.02329 17.576329233 76.47024 1.988051528 92.05852
## 2005.3260 50.02484 20.551861143 79.49782 4.949807900 95.09987
## 2005.3288 51.98681 22.487829905 81.48579 6.872013277 97.10161
## 2005.3315 44.28756 14.762605326 73.81252 -0.866962569 89.44209
## 2005.3342 37.22445 7.673540313 66.77536 -7.969766759 82.41867
## 2005.3370 46.14720 16.570353515 75.72404 0.913319322 91.38107
## 2005.3397 49.93302 20.330269882 79.53577 4.659520592 95.20652
## 2005.3425 46.54110 16.912465439 76.16974 1.228013045 91.85419
## 2005.3452 41.28752 11.633020830 70.94202 -4.065122706 86.64016
## 2005.3479 40.25724 10.576895545 69.93757 -5.134927203 85.64940
## 2005.3507 44.70684 15.000684343 74.41300 -0.724805718 90.13849
## 2005.3534 48.49030 18.758344863 78.22225 3.019199357 93.96140
## 2005.3562 44.13151 14.373781483 73.88924 -1.379007630 89.64202
## 2005.3589 40.69984 10.916357608 70.48331 -4.850063305 86.24973
## 2005.3616 52.27126 22.462048714 82.08046 6.682007776 97.86050
## 2005.3644 48.30986 18.474949535 78.14478 2.681300318 93.93843
## 2005.3671 47.92910 18.068505455 77.78970 2.261259674 93.59695
## 2005.3699 48.03246 18.146198195 77.91872 2.325367536 93.73955
## 2005.3726 46.66880 16.756899428 76.58070 0.922495544 92.41511
## 2005.3753 49.59329 19.655770674 79.53081 3.807805191 95.37878
## 2005.3781 50.46473 20.501615417 80.42785 4.640099931 96.28936
## 2005.3808 47.55460 17.565914121 77.54330 1.690860196 93.41835
## 2005.3836 45.22935 15.215106719 75.24359 -0.673474108 91.13217
## 2005.3863 50.87390 20.834124235 80.91367 4.932028012 96.81577
## 2005.3890 50.85345 20.788168445 80.91874 4.872568303 96.83434
## 2005.3918 46.97410 16.883327509 77.06487 0.954234897 92.99396
## 2005.3945 47.51414 17.397900565 77.63038 1.455326901 93.57295
## 2005.3973 49.13797 18.996288277 79.27965 3.040244951 95.23570
## 2005.4000 50.62915 20.462048290 80.79626 4.492546663 96.76576
## 2005.4027 50.39761 20.205098809 80.59012 4.222150214 96.57306
## 2005.4055 48.81289 18.595005121 79.03078 2.598620861 95.02717
## 2005.4082 48.64098 18.397727351 78.88422 2.387918702 94.89403
## 2005.4110 48.05093 17.782347749 78.31952 1.759125959 94.34274
## 2005.4137 44.79901 14.505109327 75.09292 -1.531514387 91.12954
## 2005.4164 44.52847 14.209272638 74.84767 -1.840741809 90.89769
## 2005.4192 48.34381 17.999335383 78.68828 1.935941367 94.75168
## 2005.4219 48.11349 17.743765764 78.48322 1.667003313 94.55998
## 2005.4247 52.62444 22.229476009 83.01940 6.139356231 99.10952
## 2005.4274 51.26988 20.849708762 81.69005 4.746242735 97.79352
## 2005.4301 49.88853 19.443167778 80.33389 3.326366555 96.45069
## 2005.4329 47.79433 17.323799306 78.26486 1.193673911 94.39499
## 2005.4356 47.74031 17.244627109 78.23599 1.101188540 94.37943
## 2005.4384 47.84330 17.322493535 78.36411 1.165752761 94.52085
## 2005.4411 48.48126 17.935343980 79.02718 1.765311945 95.19721
## 2005.4438 46.74444 16.173433141 77.31544 -0.009879239 93.49876
## 2005.4466 48.21585 17.619777909 78.81192 1.423196073 95.00850
## 2005.4493 50.18783 19.566717511 80.80895 3.356877081 97.01879
## 2005.4521 50.50706 19.860916773 81.15320 3.637828586 97.37629
## 2005.4548 49.80402 19.132869834 80.47517 2.896544698 96.71149
## 2005.4575 49.42998 18.733848528 80.12611 2.484297225 96.37567
## 2005.4603 48.88649 18.165393632 79.60759 1.902626921 95.87036
## 2005.4630 48.21846 17.472414180 78.96450 1.196442790 95.24047
## 2005.4658 48.20442 17.433451744 78.97538 1.144286379 95.26455
## 2005.4685 50.44060 19.644730731 81.23647 3.342382070 97.53882
## 2005.4712 51.12620 20.305441887 81.94695 3.989920582 98.26247
## 2005.4740 48.68358 17.837967680 79.52920 1.509284358 95.85789
## 2005.4767 49.86503 18.994570289 80.73549 2.652735550 97.07733
## 2005.4795 48.78316 17.887874905 79.67844 1.532899325 96.03342
## 2005.4822 47.71027 16.790185799 78.63036 0.422079928 94.99847
## 2005.4849 48.95910 18.014225937 79.90397 1.633000300 96.28520
## 2005.4877 50.28805 19.318411265 81.25768 2.924076360 97.65202
## 2005.4904 47.14507 16.150686650 78.13945 -0.256747048 94.54688
## 2005.4932 45.37714 14.358040120 76.39625 -2.062481922 92.81677
## 2005.4959 48.13629 17.092476377 79.18009 0.658876415 95.61369
## 2005.4986 49.50418 18.435684221 80.57267 1.989016737 97.01934
## 2005.5014 48.08339 16.990232548 79.17655 0.530507918 95.63628
## 2005.5041 47.07993 15.962120566 78.19773 -0.510650861 94.67050
## 2005.5068 49.22253 18.080095826 80.36496 1.594287928 96.85077
## 2005.5096 48.86524 17.698200880 80.03228 1.199366811 96.53111
## 2005.5123 46.58730 15.395671472 77.77893 -1.116178492 94.29078
## 2005.5151 49.91359 18.697394687 81.12979 2.172539080 97.65464
## 2005.5178 50.67173 19.430988372 81.91248 2.893137350 98.45033
## 2005.5205 51.13840 19.873121818 82.40367 3.322285586 98.95451
## 2005.5233 50.76686 19.477077334 82.05665 2.913266071 98.62046
## 2005.5260 49.18333 17.869057031 80.49761 1.292280891 97.07438
## 2005.5288 48.84676 17.508009334 80.18550 0.918278451 96.77524
## 2005.5315 49.37314 18.009934812 80.73634 1.407259294 97.33901
## 2005.5342 50.24134 18.853704921 81.62897 2.238094853 98.24458
## 2005.5370 49.48282 18.070766309 80.89487 1.442231752 97.52340
## 2005.5397 49.21796 17.781519049 80.65441 1.140070040 97.29586
## 2005.5425 49.54475 18.083931734 81.00558 1.429578289 97.65993
## 2005.5452 47.80338 16.318196105 79.28856 -0.349051786 95.95581
## 2005.5479 49.97938 18.469861326 81.48890 1.789728957 98.16903
## 2005.5507 48.53662 17.002784187 80.07047 0.309777285 96.76347
## 2005.5534 48.28804 16.729899442 79.84618 0.024027928 96.55206
## 2005.5562 47.18766 15.605231145 78.77008 -1.113495081 95.48881
## 2005.5589 49.47571 17.869017687 81.08240 1.137446625 97.81397
## 2005.5616 48.23248 16.601545143 79.86342 -0.142860901 96.60782
## 2005.5644 46.39473 14.739565634 78.04989 -2.017665563 94.80712
## 2005.5671 48.77722 17.097843267 80.45659 0.327796727 97.22663
## 2005.5699 49.73392 18.030355277 81.43748 1.247503179 98.22033
## 2005.5726 49.91538 18.187650460 81.64312 1.392002568 98.43877
## 2005.5753 50.09602 18.344131271 81.84791 1.535697325 98.65634
## 2005.5781 51.36684 19.590820721 83.14287 2.769610440 99.96408
## 2005.5808 48.15113 16.350988660 79.95127 -0.482988259 96.78524
## 2005.5836 49.29017 17.465932541 81.11441 0.619198659 97.96114
## 2005.5863 49.63898 17.790666129 81.48730 0.931184937 98.34678
## 2005.5890 45.87819 14.005809520 77.75057 -2.866409351 94.62279
## 2005.5918 49.47633 17.579907956 81.37276 0.694961014 98.25770
## 2005.5945 47.87939 15.958938382 79.79984 -0.938727043 96.69750
## 2005.5973 49.86734 17.922879696 81.81179 1.012505354 98.72217
## 2005.6000 51.28499 19.316540421 83.25343 2.393466706 100.17651
## 2005.6027 49.79736 17.804943623 81.78978 0.869180057 98.72555
## 2005.6055 46.90040 14.884032174 78.91678 -2.064411742 95.86522
## 2005.6082 48.17280 16.132494455 80.21311 -0.828620330 97.17423
## 2005.6110 46.08592 14.021690160 78.15014 -2.952086035 95.12392
## 2005.6137 48.61488 16.526754891 80.70301 -0.459673277 97.68944
## 2005.6164 49.04702 16.935009701 81.15903 -0.064061023 98.15810
## 2005.6192 49.24238 17.106510517 81.37826 0.094806631 98.38996
## 2005.6219 41.76949 9.609770299 73.92921 -7.414557373 90.95354
## 2005.6247 45.75414 13.570585298 77.93768 -3.466356807 94.97463
## 2005.6274 47.11822 14.910855251 79.32558 -2.138691953 96.37513
## 2005.6301 48.29373 16.062570622 80.52488 -0.999572369 97.58702
## 2005.6329 50.64259 18.387656799 82.89752 1.312927312 99.97225
## 2005.6356 50.96636 18.687669636 83.24505 1.600362926 100.33236
## 2005.6384 49.48269 17.180254984 81.78512 0.080380300 98.88499
## 2005.6411 49.68256 17.356399148 82.00871 0.243965722 99.12115
## 2005.6438 47.63864 15.288776366 79.98850 -1.836206594 97.11349
## 2005.6466 49.61110 17.237545533 81.98465 0.100022230 99.12217
## 2005.6493 48.50768 16.110453373 80.90490 -1.039601104 98.05496
## 2005.6521 48.05292 15.632044286 80.47380 -1.530532214 97.63638
## 2005.6548 49.13792 16.693405419 81.58244 -0.481683976 98.75753
## 2005.6575 46.39750 13.929368192 78.86564 -3.258224987 96.05323
## 2005.6603 42.72889 10.237151641 75.22063 -6.962936233 92.42072
## 2005.6630 45.64738 13.132059504 78.16271 -4.080513995 95.37528
## 2005.6658 48.49685 15.957956988 81.03575 -1.267093086 98.26080
## 2005.6685 42.28204 9.719590026 74.84448 -7.517927593 92.08200
## 2005.6712 44.41372 11.827739765 76.99970 -5.422236387 94.24968
## 2005.6740 45.87790 13.268403889 78.48740 -3.994021805 95.74983
## 2005.6767 38.69111 6.058106694 71.32411 -11.216759569 88.59897
## 2005.6795 41.22192 8.565435576 73.87840 -8.721862304 91.16570
## 2005.6822 43.88480 11.204845680 76.56475 -6.094874883 93.86447
## 2005.6849 41.61278 8.909377797 74.31618 -8.402756536 91.62831
## 2005.6877 38.35397 5.627134370 71.08080 -11.697404838 88.40534
## 2005.6904 40.14876 7.398510146 72.89901 -9.938425060 90.23595
## 2005.6932 38.95567 6.182016840 71.72932 -11.167305507 89.07864
## 2005.6959 34.24959 1.452553555 67.04662 -15.909147097 84.40832
## 2005.6986 43.15792 10.337517555 75.97832 -7.036552581 93.35239
## 2005.7014 36.08008 3.236330113 68.92383 -14.150100708 86.31026
## 2005.7041 36.37878 3.511695746 69.24586 -13.887086978 86.64464
## 2005.7068 38.61642 5.726016097 71.50682 -11.685109767 88.91794
## 2005.7096 43.87718 10.963476459 76.79088 -6.459983801 94.21434
## 2005.7123 41.47336 8.536375637 74.41034 -8.899410294 91.84613
## 2005.7151 35.86079 2.900541139 68.82104 -14.547561755 86.26915
## 2005.7178 34.91067 1.927166190 67.89417 -15.533244979 85.35458
## 2005.7205 38.20614 5.199398969 71.21287 -12.273311804 88.68558
## 2005.7233 43.17130 10.141342092 76.20125 -7.343659634 93.68625
## 2005.7260 46.49246 13.439306974 79.54562 -4.057977071 97.04290
## 2005.7288 44.01490 10.938553147 77.09124 -6.571004601 94.60079
## 2005.7315 35.38183 2.282320995 68.48134 -15.239501859 86.00317
## 2005.7342 41.16998 8.047315040 74.29264 -9.486764340 91.82672
## 2005.7370 30.42040 -2.725401070 63.56620 -20.271728415 81.11253
## 2005.7397 32.39939 -0.769533740 65.56831 -18.328100506 83.12688
## 2005.7425 41.97294 8.780908502 75.16496 -8.789889160 92.73576
## 2005.7452 43.17363 9.958515140 76.38875 -7.624504910 93.97177
## 2005.7479 42.78089 9.542703571 76.01908 -8.052530375 93.61431
## 2005.7507 40.05617 6.794929702 73.31742 -10.812509669 90.92486
## 2005.7534 39.00978 5.725493754 72.29406 -11.894142587 89.91370
## 2005.7562 44.20856 10.901249636 77.51587 -6.730575238 95.14769
## 2005.7589 37.85204 4.521724897 71.18236 -13.122280090 88.82637
## 2005.7616 39.70472 6.351405025 73.05803 -11.304771673 90.71421
## 2005.7644 38.59131 5.215019188 71.96760 -12.453320835 89.63594
## 2005.7671 35.28048 1.881234113 68.67973 -15.799260867 86.36023
## 2005.7699 28.16824 -5.253960196 61.59043 -22.946601784 79.28307
## 2005.7726 40.15278 6.707652937 73.59790 -10.997126924 91.30268
## 2005.7753 41.32734 7.859299566 74.79538 -9.857610252 92.51229
## 2005.7781 34.82174 1.330802879 68.31268 -16.398228597 86.04171
## 2005.7808 39.17960 5.665784061 72.69342 -12.075360792 90.43457
## 2005.7836 37.57790 4.041215865 71.11459 -13.712034099 88.86784
## 2005.7863 36.22293 2.663387229 69.78247 -15.101959597 87.54781
## 2005.7890 28.20041 -5.381960016 61.78279 -23.159395473 79.56023
## 2005.7918 25.77186 -7.833330619 59.37706 -25.622846493 77.16658
## 2005.7945 30.20640 -3.421595730 63.83441 -21.223183823 81.63599
## 2005.7973 35.98256 2.331772146 69.63335 -15.481879984 87.44700
## 2005.8000 39.63831 5.964747351 73.31188 -11.860960651 91.13758
## 2005.8027 40.50417 6.807846620 74.20049 -11.029909107 92.03825
## 2005.8055 37.55319 3.834124667 71.27226 -14.015670653 89.12205
## 2005.8082 35.18123 1.439437011 68.92303 -16.422389786 86.78485
## 2005.8110 32.81643 -0.948075646 66.58094 -18.821925822 84.45479
## 2005.8137 42.60917 8.821965547 76.39637 -9.063899925 94.28224
## 2005.8164 37.40565 3.595761440 71.21553 -14.302111263 89.11341
## 2005.8192 41.48322 7.650668407 75.31578 -10.259203477 93.22565
## 2005.8219 29.39635 -4.458856998 63.25155 -22.380720028 81.17342
## 2005.8247 36.66305 2.785205282 70.54089 -15.148640877 88.47474
## 2005.8274 37.14791 3.247444112 71.04837 -14.698377174 88.99419
## 2005.8301 43.05347 9.130399739 76.97654 -8.827388689 94.93433
## 2005.8329 40.39577 6.450111907 74.34143 -11.519635693 92.31118
## 2005.8356 26.05467 -7.913571448 60.02290 -25.895270266 78.00460
## 2005.8384 24.81776 -9.173036202 58.80856 -27.166678301 76.80220
## 2005.8411 38.73874 4.725392284 72.75208 -13.280185173 90.75766
## 2005.8438 44.05393 10.018056053 78.08981 -7.999448857 96.10731
## 2005.8466 32.61054 -1.447850418 66.66894 -19.477274888 84.69836
## 2005.8493 30.75888 -3.322011721 64.83978 -21.363347878 82.88111
## 2005.8521 23.08254 -11.020842579 57.18592 -29.074082563 75.23916
## 2005.8548 31.22730 -2.898554892 65.35315 -20.963690859 83.41829
## 2005.8575 32.26842 -1.879894413 66.41673 -19.956918534 84.49375
## 2005.8603 40.64795 6.477197531 74.81871 -11.611706932 92.90761
## 2005.8630 45.58187 11.388687982 79.77505 -6.712089025 97.87583
## 2005.8658 34.01025 -0.205346315 68.22584 -18.317988084 86.33848
## 2005.8685 34.26583 0.027833230 68.50382 -18.096665533 86.62832
## 2005.8712 32.74793 -1.512446860 67.00831 -19.648794866 85.14465
## 2005.8740 34.63272 0.349978185 68.91547 -17.798211328 87.06366
## 2005.8767 42.42436 8.119255572 76.72946 -10.040767726 94.88948
## 2005.8795 37.69305 3.365605872 72.02049 -14.806243505 90.19234
## 2005.8822 30.19451 -4.155253351 64.54428 -22.338921115 82.72795
## 2005.8849 36.92234 2.550263368 71.29442 -15.645215107 89.48990
## 2005.8877 41.84988 7.455507252 76.24425 -10.751774273 94.45154
## 2005.8904 39.62682 5.210162165 74.04347 -13.008914763 92.26255
## 2005.8932 35.64712 1.208192708 70.08604 -17.022671992 88.31690
## 2005.8959 35.61822 1.157043302 70.07940 -17.085601552 88.32204
## 2005.8986 33.41806 -1.065353099 67.90148 -19.319770506 86.15589
## 2005.9014 29.13459 -5.371052067 63.64023 -23.637234439 81.90641
## 2005.9041 36.38628 1.858429592 70.91413 -16.419510173 89.19207
## 2005.9068 33.40616 -1.143889848 67.95620 -19.433579448 86.24589
## 2005.9096 32.19031 -2.381913056 66.76254 -20.683344946 85.06397
## 2005.9123 40.26730 5.672909023 74.86170 -12.640257628 93.17487
## 2005.9151 47.97051 13.353958019 82.58706 -4.970935880 100.91195
## 2005.9178 41.01660 6.377910788 75.65529 -11.958702858 93.99190
## 2005.9205 34.66353 0.002719961 69.32435 -18.345605946 87.67267
## 2005.9233 37.60420 2.921274323 72.28712 -15.438756373 90.64715
## 2005.9260 29.73436 -4.970656216 64.43938 -23.342384244 82.81111
## 2005.9288 28.05550 -6.671602968 62.78260 -25.055020885 81.16602
## 2005.9315 33.36584 -1.383326984 68.11502 -19.778427362 86.51012
## 2005.9342 19.47529 -15.295940760 54.24651 -33.702716183 72.65329
## 2005.9370 32.52023 -2.273035793 67.31350 -20.691478862 85.73194
## 2005.9397 39.93585 5.120551921 74.75114 -13.309551406 93.18124
## 2005.9425 36.81478 1.977471812 71.65209 -16.464284402 90.09384
## 2005.9452 34.62007 -0.239236213 69.47938 -18.692637955 87.93278
## 2005.9479 33.51171 -1.369584954 68.39300 -19.834624878 86.85804
## 2005.9507 36.17356 1.270301999 71.07683 -17.206368778 89.55350
## 2005.9534 31.48523 -3.439993149 66.41045 -21.928287462 84.89874
## 2005.9562 34.96719 0.020023433 69.91435 -18.479887112 88.41426
## 2005.9589 29.21710 -5.751987749 64.18620 -24.263507238 82.69772
## 2005.9616 32.79734 -2.193665086 67.78835 -20.716786242 86.31147
## 2005.9644 36.00588 0.992972809 71.01880 -17.541742752 89.55351
## 2005.9671 35.89997 0.865165474 70.93477 -17.681137244 89.48107
## 2005.9699 30.40431 -4.652367222 65.46098 -23.210249862 84.01887
## 2005.9726 29.42862 -5.649919715 64.50715 -24.219375057 83.07661
## 2005.9753 32.24617 -2.854217935 67.34655 -21.435238771 85.92757
## 2005.9781 33.39260 -1.729617306 68.51482 -20.322196440 87.10740
## 2005.9808 32.23033 -2.913712808 67.37436 -21.517843060 85.97849
## 2005.9836 36.43058 1.264736704 71.59643 -17.350937499 90.21210
## 2005.9863 36.94264 1.754996240 72.13027 -16.872214759 90.75749
## 2005.9890 33.79272 -1.416698720 69.00214 -20.055439375 87.64088
## 2005.9918 24.27567 -10.955514100 59.50686 -29.605777283 78.15712
## 2005.9945 34.58791 -0.665032255 69.84085 -19.326810852 88.50262
## 2005.9973 35.88607 0.611393312 71.16075 -18.061893597 89.83404
## 2006.0000 37.52110 2.224693687 72.81750 -16.460094446 91.50229
## 2006.0027 44.58918 9.271058687 79.90729 -9.425223594 98.60358
## 2006.0055 34.13236 -1.207452867 69.47218 -19.915222235 88.17995##NOTE: AIC = 26480.80 , BIC = 26497.88 , RMSE = 8.932469
Also, the headline of the plot below contains ETS(A,N,N) showing that the automated model characterized error of the “tsWSR_PK” SERIES as Additative (A), trend as None (A) and seasonality as None (N) which is equivalent to simple exponential model(ses) with only alpha parameter i.e level.
#Model 2 : ARIMA Model(AutoRegressive Moving Average)
It is used for forecasting for both seasonal and non- seasonal level.
#Changing to stationary set
train.sta_Var9 <- diff(train8)
test.sta_Var9 <- diff(test8)#2.1 Auto Arima model without sesonality:
set.seed(301)
model_Var9 <- auto.arima(train.sta_Var9, seasonal = FALSE)
summary(model_Var9)## Series: train.sta_Var9
## ARIMA(2,0,1) with zero mean
##
## Coefficients:
## ar1 ar2 ma1
## 0.4594 -0.1664 -0.9394
## s.e. 0.0222 0.0219 0.0082
##
## sigma^2 estimated as 85.19: log likelihood=-7981.24
## AIC=15970.47 AICc=15970.49 BIC=15993.24
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -0.01234418 9.223455 6.571991 NaN Inf 0.6020914 0.004027249##NOTE: AIC = 15970.47 , BIC = 15993.24 , RMSE = 9.223455
tsdisplay(residuals(model_Var9), lag.max = 45, main = '(1,1,1) Model Residuals')
#2.2 Auto Arima model with sesonality:
set.seed(301)
model2_Var9 <- auto.arima(train.sta_Var9, seasonal= TRUE)
summary(model2_Var9)## Series: train.sta_Var9
## ARIMA(5,0,3) with zero mean
##
## Coefficients:
## ar1 ar2 ar3 ar4 ar5 ma1 ma2 ma3
## 0.2715 0.6444 -0.3462 0.1117 -0.019 -0.7471 -0.9168 0.6935
## s.e. 0.2485 0.1356 0.0760 0.0445 0.024 0.2478 0.0732 0.2245
##
## sigma^2 estimated as 85.21: log likelihood=-7978.98
## AIC=15975.95 AICc=15976.03 BIC=16027.18
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -0.01021262 9.213898 6.567264 NaN Inf 0.6016584 0.0006608765##NOTE: AIC = 15975.95 , BIC = 16027.18 , RMSE = 9.213898
tsdisplay(residuals(model2_Var9), lag.max = 20, main = 'Seasonal Model Residuals')
NOTE: Above Graphs does not shows any serious lags.This indicates the good fit of the model.
Fit the observed with the predicted values for both models in the same plot.
par(mfrow = c(2,2))
fit_auto_train_Var9 %>% forecast(h=341) %>% autoplot() 
model2_Var9 %>% forecast(h=341) %>% autoplot() 
model_Var9 %>% forecast(h=341) %>% autoplot() 
COMMENT:
1. The plots includes 80% to 95% confidence interval.
2. For ARIMA models it plots the forecast but because of the nature of autoregressive process, these forecast stabilizes quite smoothly.
Plot and comment on the residuals of the fitted data for both models in the same plot.
Residual Plot - to confirm no problem with this model
par(mfrow= c(2,2))
hist(fit_auto_train_Var9$residuals,col = 'red',xlab = 'Error',main = 'Histogram Of Residuals',freq= FALSE)
lines(density(fit_auto_train_Var9$residuals))
hist(model_Var9$residuals,col = 'red',xlab = 'Error',main = 'Histogram Of Residuals',freq= FALSE)
lines(density(model_Var9$residuals))
hist(model2_Var9$residuals,col = 'red',xlab = 'Error',main = 'Histogram Of Residuals',freq= FALSE)
lines(density(model2_Var9$residuals))
OBSERVATION:
The residuals for each model are normally distributed, which shows the good fit of the models.However, on comparing all three models, residuals of “model_Var9” are normally distributed.
Testing the autocorrelation and partial autocorrelation of the residuals (using the plots and Ljung-Box Q statistic) up to an appropriate lag *
- ACF & PACF Plots
par(mfrow = c(3,2))
acf(fit_auto_train_Var9$residuals, main = 'Correlogram')
pacf(fit_auto_train_Var9$residuals, main = 'Partial Corelogram')
acf(model_Var9$residuals, main = 'Correlogram')
pacf(model_Var9$residuals, main = 'Partial Corelogram')
acf(model2_Var9$residuals, main = 'Correlogram')
pacf(model2_Var9$residuals, main = 'Partial Corelogram')
NOTE:
1. Residuals are the difference between actaual and fitted values
2. These blue lines are signficance bounds
3. This graph shows us the autocorelations for insample forecast errors
4. Do not exceed these significance bounds for lags 1 to end
#Ljunx-Box Test to check the autocorelations of the residuals
HO: No serial correlation upto 20 lags (does not exhibit lack of fit of the model)
Ha: Serial corelation is present (the model exhibits lack of fit)
We reject the null hypothesis, if p value is less than 0.05. This test is generally done for ARIMA models
Box.test(model_Var9$residuals, lag =20, type = 'Ljung-Box')##
## Box-Ljung test
##
## data: model_Var9$residuals
## X-squared = 23.789, df = 20, p-value = 0.2517Box.test(model2_Var9$residuals, lag =20, type = 'Ljung-Box')##
## Box-Ljung test
##
## data: model2_Var9$residuals
## X-squared = 20.504, df = 20, p-value = 0.4268OBSERVATIONS: For above performed Ljunx-Box Test on both the ARIMA models output, we can say that p-value is more than significance level 0.05, then there is not a statistical significance.
We conclude that there is a liitle evidence of non-zero auto-corelations in the insample forecast errors at lags 1 to 20.
So we fail to rejects the null hypothesis. Hence, we conclude that there is no serial auto corelation present between lags. Hence, the model seems to be good fit.
Test and comment on the normality of the residuals.
Here, further testing the normality by plotting Normal Q-Q plots. From below plots we observed that most of the datapoints lies on the line. Hence, we could conclude that our model produces residuals that are normal
par(mfrow = c(2,2))
qqnorm(fit_auto_train_Var9$residuals)
qqnorm(model_Var9$residuals)
qqnorm(model2_Var9$residuals)
#Validating The Model by testing the model performance with Holdout set
Here, choosing RMSE as evaluation parameter. The lower RMSE indicates a more accurate forecast.
Below, is the comparison of model. We are fitting the model to test set which is the holdout set. And checking the accuracy using RMSE(Root mean square error) evaluation parameter.
accuracy(forecast(fit_auto_train_Var9), test8) ["Test set", "RMSE"]## [1] 11.11376#o/p - 11.11376
accuracy(forecast(model2_Var9), test.sta_Var9) ["Test set", "RMSE"]## [1] 9.527655#o/p - 9.527655
accuracy(forecast(model_Var9), test.sta_Var9) ["Test set", "RMSE"]## [1] 9.523064#O/P - 9.523064
NOTE:- Here, the RMSE value is less for ARIMA models compared to exponential model.
The minimum RMSE is of model_Var9. Hence, it is forecasting better than other models in comparision.
However, The RMSE of auto arima models with seasonality and without seasonality have not much difference. It gives the same result for this series.
COMMENT ON BEST MODEL AND ITS PARAMETERS
We observed the best model to be ARIMA model i.e.“model_Var9”.
summary(model_Var9)## Series: train.sta_Var9
## ARIMA(2,0,1) with zero mean
##
## Coefficients:
## ar1 ar2 ma1
## 0.4594 -0.1664 -0.9394
## s.e. 0.0222 0.0219 0.0082
##
## sigma^2 estimated as 85.19: log likelihood=-7981.24
## AIC=15970.47 AICc=15970.49 BIC=15993.24
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -0.01234418 9.223455 6.571991 NaN Inf 0.6020914 0.004027249Passing parameter order = (2,0,1) ,which means
p = 2
d = 0
q = 1
For the best model, 2 members of lag are used as a predictor. As we transformed the series to stationary so members of differences needed for stationarity is 0. 1 is the number of lagged forecasts errors used in the prediction equation.
AIC = 15970.47, RMSE = 9.223455 which is minimum as compared to other models.
10. Forecasting on Sea level pressure (SLP)
#Checking the attributes of time series
attributes(tsSLP)## $tsp
## [1] 1998.00 2004.94 365.00
##
## $class
## [1] "ts"#Plotting the series
plot(tsSLP, main = "Sea level pressure (tsSLP)", col = "red")
From the plot, we observes there might be presence of some trend and seems to have seasonlity.
Checking the statistics and visualising the missing data in the series:
#Visualising the distribution of missing data
plotNA.distribution(tsSLP)
As we observes the data is missing at random, so locf and NOCB seems the good technique to implement here.
#Impute the missing values with “na_locf” function of “imputeTS package” and visualise the imputed values in the time series
tsSLP.imp <- na_locf(tsSLP)
plotNA.imputations(tsSLP, tsSLP.imp)
#Decomposition Of Time Series
decomp9 <- decompose(tsSLP.imp)
plot(decomp9, col = "red")
OBSERVATIONS:
1)There seems to have trend.
2)We observes upward trend from year 1998 to 2001 and downward trend from year 2001 to 2003.
3)We observe some seasonality in the series. Seasonality describes cyclical effects due to the time of the year.
Let’s explore this seasonality pattern by plotting the decomp$seasonal components such that y-axis represents Seasonality Index and x-axis has month
#Plotting the decomposed series
par(mfrow =c (1,2))
plot(decomp9$seasonal, type ='b', xlab = 'Years', ylab = 'Seasonality Index', col = 'blue', las = 2, main = "SEASONAL DATA")
plot(decomp9$seasonal[1:365], type ='b', xlab = 'Years', ylab = 'Seasonality Index', col = 'blue', las = 2, main = "SEASONAL DATA")
OBSERVATIONS:
- The plot shows a strong and significant sea level presuure in winter and summer.
- Also, no increase in the transition seasons.
Stationarity check of time series
We could check the stationarity of time series by ADF and KPSS Tests:
- Augmented Dickey- Fuller(ADF) t-statistic test for unit root
- Kwiatkowski-Phillips-Schmidt-Shin (KPSS) for level or trend stationarity
adf.test(tsSLP.imp)## Warning in adf.test(tsSLP.imp): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: tsSLP.imp
## Dickey-Fuller = -7.5884, Lag order = 13, p-value = 0.01
## alternative hypothesis: stationary#p-vaue is smaller, hence it is stationary
kpss.test(tsSLP.imp, null="Trend")## Warning in kpss.test(tsSLP.imp, null = "Trend"): p-value smaller than printed p-
## value##
## KPSS Test for Trend Stationarity
##
## data: tsSLP.imp
## KPSS Trend = 0.2471, Truncation lag parameter = 8, p-value = 0.01#p-vaue is smaller, hence it is not trend stationary
NOTE: From the both tests results, it leads to CASE4, we could recheck by visualising it i.e. by plotting ACF. Second, we can check each for characteristics of stationarity by looking at the autocorrelation functions (ACF) of each signal. For a stationary signal, because we expect no dependence with time, we would expect the ACF to go to 0 for each time lag (τ). Lets visualize the signals and ACFs.
Plotting ACF to check the auto-corelations
acf(tsSLP.imp,lag.max = length(tsSLP.imp),xlab = "lag #", ylab = 'ACF',main='Statiionary Check ')
Here, we observes most of the data lies outside the blue-dotted lines means the significance level. Now, we will take the difference to make our data stationary.
It seems difference of 1 is sufficient to make the series stationary.
tsSLP.sta <- diff(tsSLP.imp)
acf(tsSLP.sta, lag.max = length(tsSLP.sta),xlab = "lag #", ylab = 'ACF',main='Statiionary Check ')
Hence, after differencing our series is now transformed to stationary time series.
#Visualising the stationary series
plot(tsSLP.sta, col = "red")
#CREATING MODELS AND FORECASTING: USING EXPONENTIAL SMOOTHING AND ARIMA TECHNIQUES FOR TIME SERIES FORECASTING
- TRAIN- TEST SET SPLIT
train9 <- window(tsSLP.imp, end = c(2004, 3))
test9 <- window(tsSLP.imp, start = c(2004, 4))#Model 1 : Auto Exponential Smoothening Model
set.seed(301)
fit_auto_train_Var10 <- forecast(train9)
summary(fit_auto_train_Var10)##
## Forecast method: STL + ETS(A,N,N)
##
## Model Information:
## ETS(A,N,N)
##
## Call:
## ets(y = na.interp(x), model = etsmodel, allow.multiplicative.trend = allow.multiplicative.trend)
##
## Smoothing parameters:
## alpha = 0.9999
##
## Initial states:
## l = 10261.7904
##
## sigma: 31.7936
##
## AIC AICc BIC
## 32047.14 32047.15 32064.22
##
## Error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -0.1105768 31.77912 22.96737 -0.001582898 0.2258044 0.4703075
## ACF1
## Training set 0.1415532
##
## Forecasts:
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 2004.0082 10091.722 10050.977 10132.47 10029.408 10154.04
## 2004.0110 10075.243 10017.624 10132.86 9987.122 10163.36
## 2004.0137 10065.387 9994.819 10135.96 9957.463 10173.31
## 2004.0164 10029.654 9948.169 10111.14 9905.034 10154.27
## 2004.0192 10031.767 9940.665 10122.87 9892.439 10171.09
## 2004.0219 10055.272 9955.475 10155.07 9902.646 10207.90
## 2004.0247 10070.099 9962.307 10177.89 9905.245 10234.95
## 2004.0274 10041.672 9926.437 10156.91 9865.435 10217.91
## 2004.0301 10024.104 9901.880 10146.33 9837.178 10211.03
## 2004.0329 10039.122 9910.286 10167.96 9842.084 10236.16
## 2004.0356 10061.980 9926.856 10197.10 9855.326 10268.63
## 2004.0384 10055.219 9914.087 10196.35 9839.376 10271.06
## 2004.0411 10029.388 9882.493 10176.28 9804.731 10254.04
## 2004.0438 10009.440 9857.000 10161.88 9776.303 10242.58
## 2004.0466 10029.907 9872.117 10187.70 9788.587 10271.23
## 2004.0493 10032.100 9869.134 10195.06 9782.866 10281.33
## 2004.0521 10061.048 9893.067 10229.03 9804.143 10317.95
## 2004.0548 10098.535 9925.684 10271.39 9834.183 10362.89
## 2004.0575 10072.787 9895.200 10250.37 9801.191 10344.38
## 2004.0603 10084.969 9902.769 10267.17 9806.318 10363.62
## 2004.0630 10078.512 9891.812 10265.21 9792.979 10364.04
## 2004.0658 10036.213 9845.119 10227.31 9743.960 10328.46
## 2004.0685 10040.598 9845.210 10235.99 9741.778 10339.42
## 2004.0712 10069.321 9869.730 10268.91 9764.073 10374.57
## 2004.0740 10048.774 9845.068 10252.48 9737.232 10360.32
## 2004.0767 10037.117 9829.376 10244.86 9719.405 10354.83
## 2004.0795 10059.187 9847.489 10270.88 9735.423 10382.95
## 2004.0822 10036.210 9820.628 10251.79 9706.505 10365.91
## 2004.0849 9992.535 9773.137 10211.93 9656.994 10328.08
## 2004.0877 10017.232 9794.084 10240.38 9675.956 10358.51
## 2004.0904 10021.562 9794.725 10248.40 9674.644 10368.48
## 2004.0932 10028.305 9797.838 10258.77 9675.836 10380.77
## 2004.0959 10042.778 9808.738 10276.82 9684.844 10400.71
## 2004.0986 10045.776 9808.216 10283.34 9682.459 10409.09
## 2004.1014 10050.357 9809.329 10291.39 9681.737 10418.98
## 2004.1041 10058.648 9814.201 10303.10 9684.798 10432.50
## 2004.1068 10055.265 9807.445 10303.08 9676.258 10434.27
## 2004.1096 10043.019 9791.874 10294.16 9658.925 10427.11
## 2004.1123 10029.918 9775.489 10284.35 9640.803 10419.03
## 2004.1151 9999.729 9742.059 10257.40 9605.657 10393.80
## 2004.1178 9995.304 9734.433 10256.17 9596.337 10394.27
## 2004.1205 10026.522 9762.488 10290.55 9622.718 10430.33
## 2004.1233 10054.495 9787.337 10321.65 9645.912 10463.08
## 2004.1260 10034.255 9764.008 10304.50 9620.948 10447.56
## 2004.1288 10026.067 9752.767 10299.37 9608.090 10444.04
## 2004.1315 9995.194 9718.874 10271.51 9572.599 10417.79
## 2004.1342 9997.537 9718.230 10276.84 9570.373 10424.70
## 2004.1370 10028.914 9746.651 10311.18 9597.230 10460.60
## 2004.1397 10055.795 9770.607 10340.98 9619.638 10491.95
## 2004.1425 10036.588 9748.504 10324.67 9596.002 10477.17
## 2004.1452 10024.230 9733.280 10315.18 9579.261 10469.20
## 2004.1479 10004.319 9710.530 10298.11 9555.008 10453.63
## 2004.1507 9975.967 9679.367 10272.57 9522.356 10429.58
## 2004.1534 9993.885 9694.500 10293.27 9536.015 10451.75
## 2004.1562 9996.275 9694.131 10298.42 9534.185 10458.37
## 2004.1589 9985.688 9680.810 10290.57 9519.416 10451.96
## 2004.1616 10006.494 9698.905 10314.08 9536.078 10476.91
## 2004.1644 10019.232 9708.956 10329.51 9544.706 10493.76
## 2004.1671 9979.492 9666.553 10292.43 9500.893 10458.09
## 2004.1699 9979.662 9664.082 10295.24 9497.024 10462.30
## 2004.1726 9999.190 9680.991 10317.39 9512.547 10485.83
## 2004.1753 10003.270 9682.474 10324.07 9512.655 10493.89
## 2004.1781 9973.023 9649.650 10296.40 9478.466 10467.58
## 2004.1808 9975.146 9649.217 10301.08 9476.681 10473.61
## 2004.1836 10014.936 9686.470 10343.40 9512.591 10517.28
## 2004.1863 10080.233 9749.251 10411.22 9574.039 10586.43
## 2004.1890 10081.442 9747.961 10414.92 9571.427 10591.46
## 2004.1918 10050.193 9714.233 10386.15 9536.386 10564.00
## 2004.1945 10037.130 9698.709 10375.55 9519.559 10554.70
## 2004.1973 10034.273 9693.408 10375.14 9512.965 10555.58
## 2004.2000 10031.458 9688.167 10374.75 9506.440 10556.48
## 2004.2027 9998.990 9653.290 10344.69 9470.288 10527.69
## 2004.2055 9953.814 9605.722 10301.91 9421.453 10486.18
## 2004.2082 9961.241 9610.773 10311.71 9425.246 10497.24
## 2004.2110 9988.131 9635.302 10340.96 9448.526 10527.74
## 2004.2137 10008.162 9652.989 10363.33 9464.971 10551.35
## 2004.2164 9997.975 9640.473 10355.48 9451.222 10544.73
## 2004.2192 9999.669 9639.853 10359.48 9449.378 10549.96
## 2004.2219 10037.442 9675.327 10399.56 9483.635 10591.25
## 2004.2247 10057.870 9693.470 10422.27 9500.569 10615.17
## 2004.2274 10053.072 9686.402 10419.74 9492.299 10613.85
## 2004.2301 10031.290 9662.363 10400.22 9467.065 10595.51
## 2004.2329 9994.823 9623.653 10365.99 9427.168 10562.48
## 2004.2356 10008.424 9635.025 10381.82 9437.360 10579.49
## 2004.2384 10013.222 9637.607 10388.84 9438.769 10587.67
## 2004.2411 9993.509 9615.691 10371.33 9415.686 10571.33
## 2004.2438 9997.599 9617.591 10377.61 9416.427 10578.77
## 2004.2466 10007.679 9625.494 10389.87 9423.177 10592.18
## 2004.2493 10016.287 9631.936 10400.64 9428.473 10604.10
## 2004.2521 9986.104 9599.600 10372.61 9394.997 10577.21
## 2004.2548 9974.317 9585.672 10362.96 9379.935 10568.70
## 2004.2575 9994.935 9604.160 10385.71 9397.296 10592.57
## 2004.2603 10024.823 9631.929 10417.72 9423.944 10625.70
## 2004.2630 10022.726 9627.726 10417.73 9418.626 10626.83
## 2004.2658 10011.593 9614.498 10408.69 9404.288 10618.90
## 2004.2685 9991.809 9592.629 10390.99 9381.316 10602.30
## 2004.2712 9992.280 9591.026 10393.53 9378.616 10605.94
## 2004.2740 10003.998 9600.681 10407.31 9387.178 10620.82
## 2004.2767 10000.009 9594.640 10405.38 9380.051 10619.97
## 2004.2795 10026.569 9619.157 10433.98 9403.487 10649.65
## 2004.2822 10023.101 9613.658 10432.54 9396.912 10649.29
## 2004.2849 10010.385 9598.920 10421.85 9381.103 10639.67
## 2004.2877 9996.607 9583.129 10410.08 9364.248 10628.97
## 2004.2904 9996.140 9580.660 10411.62 9360.719 10631.56
## 2004.2932 10001.518 9584.046 10418.99 9363.049 10639.99
## 2004.2959 9989.366 9569.910 10408.82 9347.864 10630.87
## 2004.2986 9981.059 9559.630 10402.49 9336.538 10625.58
## 2004.3014 9989.553 9566.159 10412.95 9342.027 10637.08
## 2004.3041 10003.444 9578.095 10428.79 9352.928 10653.96
## 2004.3068 10007.282 9579.986 10434.58 9353.789 10660.78
## 2004.3096 9994.869 9565.635 10424.10 9338.412 10651.33
## 2004.3123 10000.600 9569.436 10431.76 9341.192 10660.01
## 2004.3151 10001.673 9568.589 10434.76 9339.328 10664.02
## 2004.3178 9991.247 9556.251 10426.24 9325.978 10656.52
## 2004.3205 9993.830 9556.930 10430.73 9325.650 10662.01
## 2004.3233 9995.779 9556.983 10434.57 9324.699 10666.86
## 2004.3260 9990.785 9550.102 10431.47 9316.819 10664.75
## 2004.3288 9999.122 9556.560 10441.68 9322.282 10675.96
## 2004.3315 10022.692 9578.258 10467.12 9342.990 10702.39
## 2004.3342 10016.741 9570.445 10463.04 9334.189 10699.29
## 2004.3370 9997.129 9548.976 10445.28 9311.739 10682.52
## 2004.3397 9975.876 9525.876 10425.88 9287.660 10664.09
## 2004.3425 9972.995 9521.154 10424.84 9281.964 10664.03
## 2004.3452 10008.798 9555.124 10462.47 9314.964 10702.63
## 2004.3479 9998.552 9543.053 10454.05 9301.926 10695.18
## 2004.3507 9981.076 9523.758 10438.39 9281.669 10680.48
## 2004.3534 9985.707 9526.578 10444.84 9283.530 10687.88
## 2004.3562 9993.544 9532.611 10454.48 9288.607 10698.48
## 2004.3589 9975.344 9512.614 10438.07 9267.660 10683.03
## 2004.3616 9970.452 9505.932 10434.97 9260.030 10680.87
## 2004.3644 9981.491 9515.187 10447.79 9268.341 10694.64
## 2004.3671 9987.355 9519.275 10455.43 9271.488 10703.22
## 2004.3699 9981.449 9511.600 10451.30 9262.876 10700.02
## 2004.3726 9977.285 9505.672 10448.90 9256.015 10698.55
## 2004.3753 9976.672 9503.303 10450.04 9252.717 10700.63
## 2004.3781 9980.080 9504.961 10455.20 9253.448 10706.71
## 2004.3808 9991.751 9514.888 10468.61 9262.453 10721.05
## 2004.3836 9984.588 9505.989 10463.19 9252.633 10716.54
## 2004.3863 9978.438 9498.107 10458.77 9243.835 10713.04
## 2004.3890 9971.923 9489.867 10453.98 9234.683 10709.16
## 2004.3918 9980.646 9496.872 10464.42 9240.778 10720.51
## 2004.3945 9984.189 9498.703 10469.68 9241.702 10726.68
## 2004.3973 9985.440 9498.247 10472.63 9240.343 10730.54
## 2004.4000 9984.413 9495.520 10473.31 9236.716 10732.11
## 2004.4027 9982.578 9491.990 10473.17 9232.288 10732.87
## 2004.4055 9975.932 9483.655 10468.21 9223.059 10728.80
## 2004.4082 9976.285 9482.325 10470.24 9220.839 10731.73
## 2004.4110 9981.684 9486.047 10477.32 9223.673 10739.70
## 2004.4137 9979.056 9481.748 10476.37 9218.488 10739.62
## 2004.4164 9975.768 9476.793 10474.74 9212.652 10738.88
## 2004.4192 9987.543 9486.907 10488.18 9221.887 10753.20
## 2004.4219 9992.549 9490.259 10494.84 9224.363 10760.74
## 2004.4247 9991.107 9487.168 10495.05 9220.398 10761.82
## 2004.4274 9988.917 9483.333 10494.50 9215.693 10762.14
## 2004.4301 10005.768 9498.545 10512.99 9230.038 10781.50
## 2004.4329 10021.061 9512.205 10529.92 9242.833 10799.29
## 2004.4356 10026.901 9516.416 10537.39 9246.182 10807.62
## 2004.4384 10000.499 9488.391 10512.61 9217.297 10783.70
## 2004.4411 9993.378 9479.652 10507.10 9207.702 10779.05
## 2004.4438 9995.309 9479.970 10510.65 9207.166 10783.45
## 2004.4466 10007.782 9490.835 10524.73 9217.180 10798.38
## 2004.4493 10012.734 9494.185 10531.28 9219.681 10805.79
## 2004.4521 10017.521 9497.373 10537.67 9222.024 10813.02
## 2004.4548 10015.338 9493.597 10537.08 9217.404 10813.27
## 2004.4575 10022.710 9499.380 10546.04 9222.347 10823.07
## 2004.4603 10023.532 9498.620 10548.44 9220.748 10826.32
## 2004.4630 10016.269 9489.777 10542.76 9211.070 10821.47
## 2004.4658 10011.425 9483.360 10539.49 9203.819 10819.03
## 2004.4685 10011.596 9481.962 10541.23 9201.590 10821.60
## 2004.4712 10011.038 9479.839 10542.24 9198.640 10823.44
## 2004.4740 10007.009 9474.250 10539.77 9192.224 10821.79
## 2004.4767 10006.301 9471.986 10540.62 9189.137 10823.46
## 2004.4795 10017.119 9481.253 10552.98 9197.583 10836.65
## 2004.4822 10026.781 9489.369 10564.19 9204.881 10848.68
## 2004.4849 10018.937 9479.983 10557.89 9194.677 10843.20
## 2004.4877 10010.590 9470.098 10551.08 9183.979 10837.20
## 2004.4904 10004.486 9462.461 10546.51 9175.530 10833.44
## 2004.4932 10001.377 9457.823 10544.93 9170.083 10832.67
## 2004.4959 10001.496 9456.417 10546.57 9167.870 10835.12
## 2004.4986 10002.880 9456.280 10549.48 9166.928 10838.83
## 2004.5014 10004.290 9456.174 10552.41 9166.020 10842.56
## 2004.5041 10004.582 9454.954 10554.21 9163.999 10845.16
## 2004.5068 10008.735 9457.599 10559.87 9165.846 10851.62
## 2004.5096 10024.934 9472.295 10577.57 9179.746 10870.12
## 2004.5123 10020.065 9465.926 10574.20 9172.583 10867.55
## 2004.5151 10005.839 9450.205 10561.47 9156.069 10855.61
## 2004.5178 10000.523 9443.397 10557.65 9148.472 10852.57
## 2004.5205 10000.422 9441.808 10559.04 9146.096 10854.75
## 2004.5233 10003.214 9443.116 10563.31 9146.619 10859.81
## 2004.5260 9997.079 9435.501 10558.66 9138.220 10855.94
## 2004.5288 9990.041 9426.987 10553.09 9128.925 10851.16
## 2004.5315 9994.288 9429.763 10558.81 9130.921 10857.66
## 2004.5342 10003.981 9437.987 10569.97 9138.369 10869.59
## 2004.5370 10014.152 9446.694 10581.61 9146.300 10882.00
## 2004.5397 10004.604 9435.686 10573.52 9134.519 10874.69
## 2004.5425 9993.205 9422.830 10563.58 9120.891 10865.52
## 2004.5452 9990.594 9418.765 10562.42 9116.057 10865.13
## 2004.5479 9998.378 9425.100 10571.66 9121.625 10875.13
## 2004.5507 10011.893 9437.169 10586.62 9132.928 10890.86
## 2004.5534 10003.111 9426.945 10579.28 9121.941 10884.28
## 2004.5562 9995.095 9417.491 10572.70 9111.725 10878.47
## 2004.5589 10002.943 9423.903 10581.98 9117.378 10888.51
## 2004.5616 10009.816 9429.344 10590.29 9122.061 10897.57
## 2004.5644 10010.432 9428.533 10592.33 9120.494 10900.37
## 2004.5671 10008.449 9425.126 10591.77 9116.333 10900.57
## 2004.5699 10011.653 9426.908 10596.40 9117.363 10905.94
## 2004.5726 10014.235 9428.072 10600.40 9117.777 10910.69
## 2004.5753 10013.402 9425.825 10600.98 9114.781 10912.02
## 2004.5781 10014.407 9425.420 10603.39 9113.629 10915.19
## 2004.5808 10006.270 9415.875 10596.66 9103.339 10909.20
## 2004.5836 9997.285 9405.487 10589.08 9092.207 10902.36
## 2004.5863 10006.399 9413.200 10599.60 9099.179 10913.62
## 2004.5890 10017.764 9423.167 10612.36 9108.407 10927.12
## 2004.5918 10019.154 9423.163 10615.15 9107.665 10930.64
## 2004.5945 10012.502 9415.120 10609.88 9098.885 10926.12
## 2004.5973 10002.450 9403.680 10601.22 9086.711 10918.19
## 2004.6000 9998.981 9398.827 10599.14 9081.125 10916.84
## 2004.6027 9999.372 9397.836 10600.91 9079.403 10919.34
## 2004.6055 10000.718 9397.805 10603.63 9078.642 10922.79
## 2004.6082 10001.000 9396.712 10605.29 9076.821 10925.18
## 2004.6110 10006.234 9400.574 10611.89 9079.957 10932.51
## 2004.6137 10006.487 9399.458 10613.52 9078.116 10934.86
## 2004.6164 9996.248 9387.854 10604.64 9065.789 10926.71
## 2004.6192 9985.690 9375.933 10595.45 9053.147 10918.23
## 2004.6219 9994.671 9383.554 10605.79 9060.048 10929.29
## 2004.6247 9993.909 9381.436 10606.38 9057.212 10930.61
## 2004.6274 9983.652 9369.825 10597.48 9044.885 10922.42
## 2004.6301 9969.655 9354.478 10584.83 9028.823 10910.49
## 2004.6329 9976.776 9360.251 10593.30 9033.882 10919.67
## 2004.6356 9981.599 9363.730 10599.47 9036.649 10926.55
## 2004.6384 9965.202 9345.991 10584.41 9018.200 10912.20
## 2004.6411 9964.504 9343.954 10585.05 9015.455 10913.55
## 2004.6438 9980.673 9358.787 10602.56 9029.580 10931.77
## 2004.6466 9988.298 9365.079 10611.52 9035.167 10941.43
## 2004.6493 9979.885 9355.336 10604.43 9024.720 10935.05
## 2004.6521 9976.530 9350.653 10602.41 9019.334 10933.73
## 2004.6548 9978.180 9350.979 10605.38 9018.959 10937.40
## 2004.6575 9991.070 9362.547 10619.59 9029.827 10952.31
## 2004.6603 9994.148 9364.305 10623.99 9030.887 10957.41
## 2004.6630 9982.251 9351.092 10613.41 9016.977 10947.52
## 2004.6658 9973.850 9341.378 10606.32 9006.568 10941.13
## 2004.6685 9989.636 9355.854 10623.42 9020.349 10958.92
## 2004.6712 9983.209 9348.118 10618.30 9011.921 10954.50
## 2004.6740 9981.434 9345.037 10617.83 9008.149 10954.72
## 2004.6767 9989.096 9351.396 10626.79 9013.819 10964.37
## 2004.6795 9975.739 9336.740 10614.74 8998.474 10953.00
## 2004.6822 9952.052 9311.755 10592.35 8972.802 10931.30
## 2004.6849 9966.710 9325.119 10608.30 8985.481 10947.94
## 2004.6877 9992.065 9349.182 10634.95 9008.860 10975.27
## 2004.6904 10003.955 9359.781 10648.13 9018.777 10989.13
## 2004.6932 10003.516 9358.055 10648.98 9016.369 10990.66
## 2004.6959 9999.879 9353.134 10646.62 9010.768 10988.99
## 2004.6986 9995.315 9347.288 10643.34 9004.243 10986.39
## 2004.7014 9990.310 9341.004 10639.62 8997.282 10983.34
## 2004.7041 9987.340 9336.756 10637.92 8992.358 10982.32
## 2004.7068 10004.192 9352.335 10656.05 9007.262 11001.12
## 2004.7096 10007.390 9354.260 10660.52 9008.514 11006.26
## 2004.7123 10011.434 9357.035 10665.83 9010.617 11012.25
## 2004.7151 9995.684 9340.018 10651.35 8992.930 10998.44
## 2004.7178 9995.321 9338.391 10652.25 8990.633 11000.01
## 2004.7205 10010.256 9352.063 10668.45 9003.637 11016.87
## 2004.7233 10009.830 9350.377 10669.28 9001.284 11018.37
## 2004.7260 10005.418 9344.708 10666.13 8994.949 11015.89
## 2004.7288 9996.196 9334.232 10658.16 8983.809 11008.58
## 2004.7315 10020.831 9357.614 10684.05 9006.528 11035.13
## 2004.7342 10033.839 9369.372 10698.31 9017.624 11050.05
## 2004.7370 10048.582 9382.867 10714.30 9030.459 11066.71
## 2004.7397 10037.252 9370.291 10704.21 9017.223 11057.28
## 2004.7425 10028.806 9360.602 10697.01 9006.877 11050.74
## 2004.7452 10023.244 9353.799 10692.69 8999.417 11047.07
## 2004.7479 10000.145 9329.462 10670.83 8974.424 11025.87
## 2004.7507 10002.818 9330.899 10674.74 8975.206 11030.43
## 2004.7534 10013.159 9340.006 10686.31 8983.660 11042.66
## 2004.7562 10019.619 9345.233 10694.00 8988.236 11051.00
## 2004.7589 10028.618 9353.004 10704.23 8995.355 11061.88
## 2004.7616 10028.287 9351.445 10705.13 8993.146 11063.43
## 2004.7644 10010.075 9332.008 10688.14 8973.061 11047.09
## 2004.7671 10005.387 9326.097 10684.68 8966.502 11044.27
## 2004.7699 10009.607 9329.097 10690.12 8968.856 11050.36
## 2004.7726 10022.912 9341.183 10704.64 8980.297 11065.53
## 2004.7753 10034.756 9351.811 10717.70 8990.282 11079.23
## 2004.7781 10044.769 9360.610 10728.93 8998.438 11091.10
## 2004.7808 10038.720 9353.349 10724.09 8990.535 11086.91
## 2004.7836 10037.199 9350.618 10723.78 8987.164 11087.23
## 2004.7863 10033.306 9345.518 10721.10 8981.424 11085.19
## 2004.7890 10061.768 9372.774 10750.76 9008.042 11115.49
## 2004.7918 10085.104 9394.906 10775.30 9029.537 11140.67
## 2004.7945 10083.046 9391.647 10774.45 9025.642 11140.45
## 2004.7973 10077.970 9385.371 10770.57 9018.732 11137.21
## 2004.8000 10060.887 9367.091 10754.68 8999.818 11121.96
## 2004.8027 10047.291 9352.300 10742.28 8984.394 11110.19
## 2004.8055 10063.800 9367.615 10759.98 8999.078 11128.52
## 2004.8082 10064.381 9367.006 10761.76 8997.838 11130.92
## 2004.8110 10067.327 9368.763 10765.89 8998.965 11135.69
## 2004.8137 10020.251 9320.500 10720.00 8950.074 11090.43
## 2004.8164 10027.278 9326.342 10728.21 8955.288 11099.27
## 2004.8192 10030.949 9328.829 10733.07 8957.150 11104.75
## 2004.8219 10024.192 9320.891 10727.49 8948.587 11099.80
## 2004.8247 10056.264 9351.785 10760.74 8978.856 11133.67
## 2004.8274 10044.581 9338.925 10750.24 8965.373 11123.79
## 2004.8301 10038.023 9331.191 10744.85 8957.017 11119.03
## 2004.8329 10027.330 9319.325 10735.33 8944.530 11110.13
## 2004.8356 10062.992 9353.816 10772.17 8978.401 11147.58
## 2004.8384 10064.429 9354.083 10774.77 8978.049 11150.81
## 2004.8411 10026.766 9315.254 10738.28 8938.602 11114.93
## 2004.8438 10035.869 9323.191 10748.55 8945.922 11125.82
## 2004.8466 10069.399 9355.557 10783.24 8977.672 11161.13
## 2004.8493 10093.408 9378.405 10808.41 8999.905 11186.91
## 2004.8521 10091.462 9375.299 10807.63 8996.185 11186.74
## 2004.8548 10070.571 9353.250 10787.89 8973.523 11167.62
## 2004.8575 10068.548 9350.070 10787.02 8969.732 11167.36
## 2004.8603 10030.662 9311.031 10750.29 8930.081 11131.24
## 2004.8630 9990.480 9269.697 10711.26 8888.137 11092.82
## 2004.8658 10010.923 9288.989 10732.86 8906.820 11115.03
## 2004.8685 10043.698 9320.615 10766.78 8937.839 11149.56
## 2004.8712 10052.981 9328.751 10777.21 8945.367 11160.59
## 2004.8740 10048.018 9322.643 10773.39 8938.653 11157.38
## 2004.8767 10037.934 9311.416 10764.45 8926.821 11149.05
## 2004.8795 10062.520 9334.861 10790.18 8949.662 11175.38
## 2004.8822 10067.274 9338.475 10796.07 8952.673 11181.88
## 2004.8849 10062.958 9333.021 10792.89 8946.616 11179.30
## 2004.8877 10049.891 9318.818 10780.96 8931.812 11167.97
## 2004.8904 10046.852 9314.645 10779.06 8927.038 11166.67
## 2004.8932 10063.268 9329.928 10796.61 8941.721 11184.81
## 2004.8959 10054.851 9320.381 10789.32 8931.575 11178.13
## 2004.8986 10061.361 9325.761 10796.96 8936.358 11186.36
## 2004.9014 10039.769 9303.042 10776.50 8913.042 11166.50
## 2004.9041 10046.557 9308.705 10784.41 8918.109 11175.01
## 2004.9068 10037.986 9299.010 10776.96 8907.819 11168.15
## 2004.9096 10045.275 9305.176 10785.37 8913.391 11177.16
## 2004.9123 10030.917 9289.698 10772.14 8897.320 11164.51
## 2004.9151 10001.777 9259.439 10744.12 8866.469 11137.09
## 2004.9178 10022.099 9278.644 10765.55 8885.083 11159.12
## 2004.9205 10029.009 9284.438 10773.58 8890.286 11167.73
## 2004.9233 10047.419 9301.734 10793.10 8906.993 11187.85
## 2004.9260 10065.511 9318.714 10812.31 8923.384 11207.64
## 2004.9288 10066.752 9318.845 10814.66 8922.927 11210.58
## 2004.9315 10049.229 9300.213 10798.24 8903.708 11194.75
## 2004.9342 10082.606 9332.483 10832.73 8935.392 11229.82
## 2004.9370 10064.194 9312.965 10815.42 8915.289 11213.10
## 2004.9397 10064.438 9312.105 10816.77 8913.844 11215.03
## 2004.9425 10056.260 9302.825 10809.69 8903.980 11208.54
## 2004.9452 10069.058 9314.522 10823.59 8915.095 11223.02
## 2004.9479 10070.393 9314.758 10826.03 8914.749 11226.04
## 2004.9507 10066.078 9309.346 10822.81 8908.756 11223.40
## 2004.9534 10071.786 9313.958 10829.61 8912.788 11230.78
## 2004.9562 10066.063 9307.140 10824.99 8905.391 11226.73
## 2004.9589 10073.946 9313.930 10833.96 8911.602 11236.29
## 2004.9616 10073.379 9312.273 10834.49 8909.367 11237.39
## 2004.9644 10073.981 9311.785 10836.18 8908.302 11239.66
## 2004.9671 10077.150 9313.866 10840.43 8909.808 11244.49
## 2004.9699 10105.396 9341.026 10869.77 8936.392 11274.40
## 2004.9726 10117.362 9351.907 10882.82 8946.699 11288.03
## 2004.9753 10104.318 9337.778 10870.86 8931.997 11276.64
## 2004.9781 10079.751 9312.130 10847.37 8905.776 11253.73
## 2004.9808 10054.534 9285.833 10823.24 8878.907 11230.16
## 2004.9836 10039.199 9269.418 10808.98 8861.921 11216.48
## 2004.9863 10048.477 9277.619 10819.33 8869.551 11227.40
## 2004.9890 10052.697 9280.763 10824.63 8872.126 11233.27
## 2004.9918 10066.834 9293.826 10839.84 8884.620 11249.05
## 2004.9945 10069.695 9295.614 10843.78 8885.840 11253.55
## 2004.9973 10087.467 9312.315 10862.62 8901.974 11272.96
## 2005.0000 10064.366 9288.144 10840.59 8877.237 11251.50
## 2005.0027 10067.201 9289.910 10844.49 8878.438 11255.96
## 2005.0055 10075.013 9296.655 10853.37 8884.618 11265.41
## 2005.0082 10091.722 9312.299 10871.15 8899.698 11283.75
## 2005.0110 10075.243 9294.756 10855.73 8881.591 11268.90
## 2005.0137 10065.387 9283.838 10846.94 8870.110 11260.66
## 2005.0164 10029.654 9247.043 10812.26 8832.754 11226.55
## 2005.0192 10031.767 9248.096 10815.44 8833.246 11230.29
## 2005.0219 10055.272 9270.543 10840.00 8855.132 11255.41
## 2005.0247 10070.099 9284.314 10855.89 8868.344 11271.86
## 2005.0274 10041.672 9254.830 10828.51 8838.302 11245.04
## 2005.0301 10024.104 9236.209 10812.00 8819.122 11229.09
## 2005.0329 10039.122 9250.174 10828.07 8832.530 11245.71
## 2005.0356 10061.980 9271.981 10851.98 8853.781 11270.18
## 2005.0384 10055.219 9264.170 10846.27 8845.414 11265.02
## 2005.0411 10029.388 9237.291 10821.49 8817.979 11240.80
## 2005.0438 10009.440 9216.296 10802.58 8796.430 11222.45
## 2005.0466 10029.907 9235.717 10824.10 8815.298 11244.52
## 2005.0493 10032.100 9236.865 10827.33 8815.893 11248.31
## 2005.0521 10061.048 9264.770 10857.33 8843.247 11278.85
## 2005.0548 10098.535 9301.216 10895.85 8879.141 11317.93
## 2005.0575 10072.787 9274.428 10871.15 8851.802 11293.77
## 2005.0603 10084.969 9285.571 10884.37 8862.395 11307.54
## 2005.0630 10078.512 9278.076 10878.95 8854.351 11302.67
## 2005.0658 10036.213 9234.741 10837.68 8810.467 11261.96
## 2005.0685 10040.598 9238.092 10843.10 8813.271 11267.93
## 2005.0712 10069.321 9265.781 10872.86 8840.412 11298.23
## 2005.0740 10048.774 9244.202 10853.35 8818.287 11279.26
## 2005.0767 10037.117 9231.514 10842.72 8805.053 11269.18
## 2005.0795 10059.187 9252.554 10865.82 8825.549 11292.82
## 2005.0822 10036.210 9228.549 10843.87 8801.000 11271.42
## 2005.0849 9992.535 9183.847 10801.22 8755.754 11229.32
## 2005.0877 10017.232 9207.519 10826.95 8778.883 11255.58
## 2005.0904 10021.562 9210.825 10832.30 8781.646 11261.48
## 2005.0932 10028.305 9216.544 10840.07 8786.824 11269.79
## 2005.0959 10042.778 9229.996 10855.56 8799.735 11285.82
## 2005.0986 10045.776 9231.973 10859.58 8801.172 11290.38
## 2005.1014 10050.357 9235.536 10865.18 8804.195 11296.52
## 2005.1041 10058.648 9242.808 10874.49 8810.929 11306.37
## 2005.1068 10055.265 9238.408 10872.12 8805.990 11304.54
## 2005.1096 10043.019 9225.147 10860.89 8792.192 11293.85
## 2005.1123 10029.918 9211.032 10848.80 8777.540 11282.30
## 2005.1151 9999.729 9179.830 10819.63 8745.802 11253.66
## 2005.1178 9995.304 9174.394 10816.21 8739.830 11250.78
## 2005.1205 10026.522 9204.601 10848.44 8769.502 11283.54
## 2005.1233 10054.495 9231.565 10877.42 8795.932 11313.06
## 2005.1260 10034.255 9210.317 10858.19 8774.151 11294.36
## 2005.1288 10026.067 9201.122 10851.01 8764.423 11287.71
## 2005.1315 9995.194 9169.245 10821.14 8732.013 11258.38
## 2005.1342 9997.537 9170.583 10824.49 8732.820 11262.25
## 2005.1370 10028.914 9200.957 10856.87 8762.663 11295.16
## 2005.1397 10055.795 9226.837 10884.75 8788.013 11323.58
## 2005.1425 10036.588 9206.629 10866.55 8767.275 11305.90
## 2005.1452 10024.230 9193.272 10855.19 8753.389 11295.07
## 2005.1479 10004.319 9172.362 10836.28 8731.951 11276.69
## 2005.1507 9975.967 9143.013 10808.92 8702.074 11249.86
## 2005.1534 9993.885 9159.935 10827.83 8718.469 11269.30
## 2005.1562 9996.275 9161.331 10831.22 8719.339 11273.21
## 2005.1589 9985.688 9149.751 10821.63 8707.233 11264.14
## 2005.1616 10006.494 9169.565 10843.42 8726.521 11286.47
## 2005.1644 10019.232 9181.311 10857.15 8737.743 11300.72
## 2005.1671 9979.492 9140.581 10818.40 8696.489 11262.49
## 2005.1699 9979.662 9139.762 10819.56 8695.147 11264.18
## 2005.1726 9999.190 9158.303 10840.08 8713.164 11285.21
## 2005.1753 10003.270 9161.397 10845.14 8715.737 11290.80
## 2005.1781 9973.023 9130.164 10815.88 8683.982 11262.06
## 2005.1808 9975.146 9131.304 10818.99 8684.601 11265.69
## 2005.1836 10014.936 9170.110 10859.76 8722.887 11306.98
## 2005.1863 10080.233 9234.426 10926.04 8786.683 11373.78
## 2005.1890 10081.442 9234.654 10928.23 8786.392 11376.49
## 2005.1918 10050.193 9202.426 10897.96 8753.645 11346.74
## 2005.1945 10037.130 9188.384 10885.88 8739.085 11335.17
## 2005.1973 10034.273 9184.550 10884.00 8734.734 11333.81
## 2005.2000 10031.458 9180.759 10882.16 8730.427 11332.49
## 2005.2027 9998.990 9147.316 10850.66 8696.467 11301.51
## 2005.2055 9953.814 9101.166 10806.46 8649.802 11257.83
## 2005.2082 9961.241 9107.620 10814.86 8655.741 11266.74
## 2005.2110 9988.131 9133.538 10842.72 8681.144 11295.12
## 2005.2137 10008.162 9152.599 10863.72 8699.691 11316.63
## 2005.2164 9997.975 9141.442 10854.51 8688.021 11307.93
## 2005.2192 9999.669 9142.168 10857.17 8688.234 11311.10
## 2005.2219 10037.442 9178.974 10895.91 8724.529 11350.36
## 2005.2247 10057.870 9198.436 10917.30 8743.479 11372.26
## 2005.2274 10053.072 9192.673 10913.47 8737.205 11368.94
## 2005.2301 10031.290 9169.926 10892.65 8713.948 11348.63
## 2005.2329 9994.823 9132.496 10857.15 8676.008 11313.64
## 2005.2356 10008.424 9145.135 10871.71 8688.138 11328.71
## 2005.2384 10013.222 9148.973 10877.47 8691.467 11334.98
## 2005.2411 9993.509 9128.300 10858.72 8670.286 11316.73
## 2005.2438 9997.599 9131.431 10863.77 8672.910 11322.29
## 2005.2466 10007.679 9140.554 10874.80 8681.526 11333.83
## 2005.2493 10016.287 9148.205 10884.37 8688.671 11343.90
## 2005.2521 9986.104 9117.067 10855.14 8657.026 11315.18
## 2005.2548 9974.317 9104.326 10844.31 8643.780 11304.85
## 2005.2575 9994.935 9123.990 10865.88 8662.940 11326.93
## 2005.2603 10024.823 9152.925 10896.72 8691.370 11358.27
## 2005.2630 10022.726 9149.878 10895.58 8687.819 11357.63
## 2005.2658 10011.593 9137.794 10885.39 8675.233 11347.95
## 2005.2685 9991.809 9117.061 10866.56 8653.997 11329.62
## 2005.2712 9992.280 9116.583 10867.98 8653.017 11331.54
## 2005.2740 10003.998 9127.354 10880.64 8663.286 11344.71
## 2005.2767 10000.009 9122.419 10877.60 8657.851 11342.17
## 2005.2795 10026.569 9148.033 10905.10 8682.965 11370.17
## 2005.2822 10023.101 9143.622 10902.58 8678.054 11368.15
## 2005.2849 10010.385 9129.963 10890.81 8663.895 11356.88
## 2005.2877 9996.607 9115.242 10877.97 8648.676 11344.54
## 2005.2904 9996.140 9113.834 10878.45 8646.770 11345.51
## 2005.2932 10001.518 9118.272 10884.76 8650.710 11352.33
## 2005.2959 9989.366 9105.181 10873.55 8637.122 11341.61
## 2005.2986 9981.059 9095.936 10866.18 8627.380 11334.74
## 2005.3014 9989.553 9103.493 10875.61 8634.441 11344.67
## 2005.3041 10003.444 9116.448 10890.44 8646.900 11359.99
## 2005.3068 10007.282 9119.351 10895.21 8649.308 11365.26
## 2005.3096 9994.869 9106.003 10883.73 8635.466 11354.27
## 2005.3123 10000.600 9110.801 10890.40 8639.770 11361.43
## 2005.3151 10001.673 9110.942 10892.40 8639.417 11363.93
## 2005.3178 9991.247 9099.585 10882.91 8627.567 11354.93
## 2005.3205 9993.830 9101.238 10886.42 8628.728 11358.93
## 2005.3233 9995.779 9102.257 10889.30 8629.255 11362.30
## 2005.3260 9990.785 9096.334 10885.23 8622.841 11358.73
## 2005.3288 9999.122 9103.745 10894.50 8629.760 11368.48
## 2005.3315 10022.692 9126.388 10919.00 8651.913 11393.47
## 2005.3342 10016.741 9119.512 10913.97 8644.547 11388.94
## 2005.3370 9997.129 9098.975 10895.28 8623.521 11370.74
## 2005.3397 9975.876 9076.798 10874.95 8600.855 11350.90
## 2005.3425 9972.995 9072.995 10873.00 8596.564 11349.43
## 2005.3452 10008.798 9107.876 10909.72 8630.957 11386.64
## 2005.3479 9998.552 9096.710 10900.39 8619.303 11377.80
## 2005.3507 9981.076 9078.314 10883.84 8600.421 11361.73
## 2005.3534 9985.707 9082.026 10889.39 8603.646 11367.77
## 2005.3562 9993.544 9088.945 10898.14 8610.079 11377.01
## 2005.3589 9975.344 9069.828 10880.86 8590.477 11360.21
## 2005.3616 9970.452 9064.020 10876.88 8584.184 11356.72
## 2005.3644 9981.491 9074.143 10888.84 8593.823 11369.16
## 2005.3671 9987.355 9079.093 10895.62 8598.289 11376.42
## 2005.3699 9981.449 9072.274 10890.62 8590.986 11371.91
## 2005.3726 9977.285 9067.197 10887.37 8585.426 11369.14
## 2005.3753 9976.672 9065.674 10887.67 8583.420 11369.92
## 2005.3781 9980.080 9068.171 10891.99 8585.435 11374.72
## 2005.3808 9991.751 9078.932 10904.57 8595.715 11387.79
## 2005.3836 9984.588 9070.861 10898.32 8587.163 11382.01
## 2005.3863 9978.438 9063.802 10893.07 8579.624 11377.25
## 2005.3890 9971.923 9056.380 10887.46 8571.722 11372.12
## 2005.3918 9980.646 9064.198 10897.09 8579.059 11382.23
## 2005.3945 9984.189 9066.836 10901.54 8581.218 11387.16
## 2005.3973 9985.440 9067.183 10903.70 8581.086 11389.79
## 2005.4000 9984.413 9065.252 10903.57 8578.678 11390.15
## 2005.4027 9982.578 9062.515 10902.64 8575.462 11389.69
## 2005.4055 9975.932 9054.967 10896.90 8567.437 11384.43
## 2005.4082 9976.285 9054.419 10898.15 8566.413 11386.16
## 2005.4110 9981.684 9058.919 10904.45 8570.436 11392.93
## 2005.4137 9979.056 9055.392 10902.72 8566.434 11391.68
## 2005.4164 9975.768 9051.206 10900.33 8561.772 11389.76
## 2005.4192 9987.543 9062.083 10913.00 8572.174 11402.91
## 2005.4219 9992.549 9066.193 10918.91 8575.810 11409.29
## 2005.4247 9991.107 9063.856 10918.36 8572.999 11409.22
## 2005.4274 9988.917 9060.771 10917.06 8569.440 11408.39
## 2005.4301 10005.768 9076.728 10934.81 8584.924 11426.61
## 2005.4329 10021.061 9091.129 10950.99 8598.852 11443.27
## 2005.4356 10026.901 9096.076 10957.73 8603.327 11450.47
## 2005.4384 10000.499 9068.783 10932.21 8575.562 11425.44
## 2005.4411 9993.378 9060.772 10925.98 8567.080 11419.68
## 2005.4438 9995.309 9061.813 10928.80 8567.650 11422.97
## 2005.4466 10007.782 9073.398 10942.17 8578.765 11436.80
## 2005.4493 10012.734 9077.462 10948.01 8582.359 11443.11
## 2005.4521 10017.521 9081.362 10953.68 8585.789 11449.25
## 2005.4548 10015.338 9078.293 10952.38 8582.251 11448.42
## 2005.4575 10022.710 9084.779 10960.64 8588.269 11457.15
## 2005.4603 10023.532 9084.717 10962.35 8587.739 11459.33
## 2005.4630 10016.269 9076.570 10955.97 8579.124 11453.41
## 2005.4658 10011.425 9070.844 10952.01 8572.930 11449.92
## 2005.4685 10011.596 9070.133 10953.06 8571.753 11451.44
## 2005.4712 10011.038 9068.694 10953.38 8569.847 11452.23
## 2005.4740 10007.009 9063.784 10950.23 8564.471 11449.55
## 2005.4767 10006.301 9062.197 10950.40 8562.418 11450.18
## 2005.4795 10017.119 9072.136 10962.10 8571.893 11462.35
## 2005.4822 10026.781 9080.921 10972.64 8580.213 11473.35
## 2005.4849 10018.937 9072.199 10965.67 8571.027 11466.85
## 2005.4877 10010.590 9062.976 10958.20 8561.340 11459.84
## 2005.4904 10004.486 9055.997 10952.98 8553.897 11455.07
## 2005.4932 10001.377 9052.013 10950.74 8549.451 11453.30
## 2005.4959 10001.496 9051.258 10951.73 8548.233 11454.76
## 2005.4986 10002.880 9051.769 10953.99 8548.282 11457.48
## 2005.5014 10004.290 9052.307 10956.27 8548.358 11460.22
## 2005.5041 10004.582 9051.728 10957.44 8547.317 11461.85
## 2005.5068 10008.735 9055.010 10962.46 8550.139 11467.33
## 2005.5096 10024.934 9070.340 10979.53 8565.008 11484.86
## 2005.5123 10020.065 9064.602 10975.53 8558.810 11481.32
## 2005.5151 10005.839 9049.508 10962.17 8543.256 11468.42
## 2005.5178 10000.523 9043.324 10957.72 8536.614 11464.43
## 2005.5205 10000.422 9042.357 10958.49 8535.187 11465.66
## 2005.5233 10003.214 9044.283 10962.15 8536.655 11469.77
## 2005.5260 9997.079 9037.282 10956.88 8529.197 11464.96
## 2005.5288 9990.041 9029.380 10950.70 8520.837 11459.24
## 2005.5315 9994.288 9032.764 10955.81 8523.764 11464.81
## 2005.5342 10003.981 9041.594 10966.37 8532.137 11475.83
## 2005.5370 10014.152 9050.903 10977.40 8540.990 11487.31
## 2005.5397 10004.604 9040.494 10968.71 8530.125 11479.08
## 2005.5425 9993.205 9028.235 10958.18 8517.410 11469.00
## 2005.5452 9990.594 9024.763 10956.42 8513.484 11467.70
## 2005.5479 9998.378 9031.689 10965.07 8519.955 11476.80
## 2005.5507 10011.893 9044.345 10979.44 8532.157 11491.63
## 2005.5534 10003.111 9034.706 10971.52 8522.064 11484.16
## 2005.5562 9995.095 9025.834 10964.36 8512.738 11477.45
## 2005.5589 10002.943 9032.826 10973.06 8519.277 11486.61
## 2005.5616 10009.816 9038.844 10980.79 8524.842 11494.79
## 2005.5644 10010.432 9038.606 10982.26 8524.152 11496.71
## 2005.5671 10008.449 9035.769 10981.13 8520.863 11496.04
## 2005.5699 10011.653 9038.120 10985.19 8522.763 11500.54
## 2005.5726 10014.235 9039.849 10988.62 8524.041 11504.43
## 2005.5753 10013.402 9038.165 10988.64 8521.906 11504.90
## 2005.5781 10014.407 9038.320 10990.49 8521.610 11507.20
## 2005.5808 10006.270 9029.333 10983.21 8512.174 11500.37
## 2005.5836 9997.285 9019.499 10975.07 8501.890 11492.68
## 2005.5863 10006.399 9027.765 10985.03 8509.707 11503.09
## 2005.5890 10017.764 9038.282 10997.25 8519.775 11515.75
## 2005.5918 10019.154 9038.825 10999.48 8519.870 11518.44
## 2005.5945 10012.502 9031.326 10993.68 8511.923 11513.08
## 2005.5973 10002.450 9020.429 10984.47 8500.578 11504.32
## 2005.6000 9998.981 9016.115 10981.85 8495.818 11502.14
## 2005.6027 9999.372 9015.662 10983.08 8494.917 11503.83
## 2005.6055 10000.718 9016.165 10985.27 8494.974 11506.46
## 2005.6082 10001.000 9015.605 10986.40 8493.968 11508.03
## 2005.6110 10006.234 9019.997 10992.47 8497.914 11514.55
## 2005.6137 10006.487 9019.408 10993.57 8496.880 11516.09
## 2005.6164 9996.248 9008.329 10984.17 8485.357 11507.14
## 2005.6192 9985.690 8996.931 10974.45 8473.514 11497.87
## 2005.6219 9994.671 9005.073 10984.27 8481.212 11508.13
## 2005.6247 9993.909 9003.473 10984.34 8479.168 11508.65
## 2005.6274 9983.652 8992.378 10974.93 8467.630 11499.67
## 2005.6301 9969.655 8977.544 10961.77 8452.353 11486.96
## 2005.6329 9976.776 8983.829 10969.72 8458.195 11495.36
## 2005.6356 9981.599 8987.817 10975.38 8461.741 11501.46
## 2005.6384 9965.202 8970.585 10959.82 8444.067 11486.34
## 2005.6411 9964.504 8969.053 10959.96 8442.094 11486.92
## 2005.6438 9980.673 8984.388 10976.96 8456.987 11504.36
## 2005.6466 9988.298 8991.182 10985.42 8463.340 11513.26
## 2005.6493 9979.885 8981.936 10977.83 8453.654 11506.12
## 2005.6521 9976.530 8977.750 10975.31 8449.028 11504.03
## 2005.6548 9978.180 8978.570 10977.79 8449.408 11506.95
## 2005.6575 9991.070 8990.629 10991.51 8461.028 11521.11
## 2005.6603 9994.148 8992.878 10995.42 8462.837 11525.46
## 2005.6630 9982.251 8980.152 10984.35 8449.674 11514.83
## 2005.6658 9973.850 8970.924 10976.78 8440.007 11507.69
## 2005.6685 9989.636 8985.883 10993.39 8454.528 11524.74
## 2005.6712 9983.209 8978.629 10987.79 8446.837 11519.58
## 2005.6740 9981.434 8976.028 10986.84 8443.798 11519.07
## 2005.6767 9989.096 8982.865 10995.33 8450.198 11527.99
## 2005.6795 9975.739 8968.684 10982.79 8435.581 11515.90
## 2005.6822 9952.052 8944.173 10959.93 8410.634 11493.47
## 2005.6849 9966.710 8958.008 10975.41 8424.034 11509.39
## 2005.6877 9992.065 8982.541 11001.59 8448.131 11536.00
## 2005.6904 10003.955 8993.609 11014.30 8458.764 11549.15
## 2005.6932 10003.516 8992.348 11014.68 8457.069 11549.96
## 2005.6959 9999.879 8987.891 11011.87 8452.177 11547.58
## 2005.6986 9995.315 8982.507 11008.12 8446.359 11544.27
## 2005.7014 9990.310 8976.684 11003.94 8440.102 11540.52
## 2005.7041 9987.340 8972.895 11001.78 8435.880 11538.80
## 2005.7068 10004.192 8988.929 11019.45 8451.482 11556.90
## 2005.7096 10007.390 8991.310 11023.47 8453.429 11561.35
## 2005.7123 10011.434 8994.538 11028.33 8456.225 11566.64
## 2005.7151 9995.684 8977.972 11013.40 8439.228 11552.14
## 2005.7178 9995.321 8976.794 11013.85 8437.618 11553.02
## 2005.7205 10010.256 8990.914 11029.60 8451.307 11569.20
## 2005.7233 10009.830 8989.674 11029.99 8449.636 11570.02
## 2005.7260 10005.418 8984.449 11026.39 8443.981 11566.85
## 2005.7288 9996.196 8974.415 11017.98 8433.517 11558.88
## 2005.7315 10020.831 8998.238 11043.42 8456.909 11584.75
## 2005.7342 10033.839 9010.435 11057.24 8468.677 11599.00
## 2005.7370 10048.582 9024.367 11072.80 8482.180 11614.98
## 2005.7397 10037.252 9012.226 11062.28 8469.611 11604.89
## 2005.7425 10028.806 9002.972 11054.64 8459.928 11597.68
## 2005.7452 10023.244 8996.601 11049.89 8453.129 11593.36
## 2005.7479 10000.145 8972.694 11027.60 8428.794 11571.50
## 2005.7507 10002.818 8974.559 11031.08 8430.232 11575.40
## 2005.7534 10013.159 8984.094 11042.22 8439.339 11586.98
## 2005.7562 10019.619 8989.747 11049.49 8444.566 11594.67
## 2005.7589 10028.618 8997.941 11059.30 8452.334 11604.90
## 2005.7616 10028.287 8996.805 11059.77 8450.771 11605.80
## 2005.7644 10010.075 8977.789 11042.36 8431.330 11588.82
## 2005.7671 10005.387 8972.297 11038.48 8425.412 11585.36
## 2005.7699 10009.607 8975.714 11043.50 8428.404 11590.81
## 2005.7726 10022.912 8988.216 11057.61 8440.481 11605.34
## 2005.7753 10034.756 8999.259 11070.25 8451.100 11618.41
## 2005.7781 10044.769 9008.471 11081.07 8459.888 11629.65
## 2005.7808 10038.720 9001.621 11075.82 8452.614 11624.83
## 2005.7836 10037.199 8999.300 11075.10 8449.870 11624.53
## 2005.7863 10033.306 8994.608 11072.00 8444.755 11621.86
## 2005.7890 10061.768 9022.271 11101.27 8471.995 11651.54
## 2005.7918 10085.104 9044.809 11125.40 8494.110 11676.10
## 2005.7945 10083.046 9041.954 11124.14 8490.833 11675.26
## 2005.7973 10077.970 9036.081 11119.86 8484.538 11671.40
## 2005.8000 10060.887 9018.202 11103.57 8466.238 11655.54
## 2005.8027 10047.291 9003.810 11090.77 8451.425 11643.16
## 2005.8055 10063.800 9019.523 11108.08 8466.717 11660.88
## 2005.8082 10064.381 9019.311 11109.45 8466.084 11662.68
## 2005.8110 10067.327 9021.463 11113.19 8467.816 11666.84
## 2005.8137 10020.251 8973.594 11066.91 8419.527 11620.98
## 2005.8164 10027.278 8979.828 11074.73 8425.341 11629.21
## 2005.8192 10030.949 8982.706 11079.19 8427.800 11634.10
## 2005.8219 10024.192 8975.158 11073.23 8419.833 11628.55
## 2005.8247 10056.264 9006.440 11106.09 8450.696 11661.83
## 2005.8274 10044.581 8993.967 11095.20 8437.805 11651.36
## 2005.8301 10038.023 8986.618 11089.43 8430.038 11646.01
## 2005.8329 10027.330 8975.137 11079.52 8418.139 11636.52
## 2005.8356 10062.992 9010.010 11115.97 8452.595 11673.39
## 2005.8384 10064.429 9010.659 11118.20 8452.827 11676.03
## 2005.8411 10026.766 8972.209 11081.32 8413.961 11639.57
## 2005.8438 10035.869 8980.526 11091.21 8421.860 11649.88
## 2005.8466 10069.399 9013.269 11125.53 8454.188 11684.61
## 2005.8493 10093.408 9036.493 11150.32 8476.996 11709.82
## 2005.8521 10091.462 9033.762 11149.16 8473.849 11709.08
## 2005.8548 10070.571 9012.086 11129.06 8451.758 11689.38
## 2005.8575 10068.548 9009.279 11127.82 8448.536 11688.56
## 2005.8603 10030.662 8970.610 11090.71 8409.453 11651.87
## 2005.8630 9990.480 8929.646 11051.31 8368.074 11612.89
## 2005.8658 10010.923 8949.307 11072.54 8387.321 11634.53
## 2005.8685 10043.698 8981.301 11106.10 8418.901 11668.50
## 2005.8712 10052.981 8989.802 11116.16 8426.989 11678.97
## 2005.8740 10048.018 8984.059 11111.98 8420.833 11675.20
## 2005.8767 10037.934 8973.195 11102.67 8409.557 11666.31
## 2005.8795 10062.520 8997.003 11128.04 8432.952 11692.09
## 2005.8822 10067.274 9000.978 11133.57 8436.515 11698.03
## 2005.8849 10062.958 8995.883 11130.03 8431.008 11694.91
## 2005.8877 10049.891 8982.039 11117.74 8416.752 11683.03
## 2005.8904 10046.852 8978.223 11115.48 8412.525 11681.18
## 2005.8932 10063.268 8993.862 11132.67 8427.754 11698.78
## 2005.8959 10054.851 8984.670 11125.03 8418.151 11691.55
## 2005.8986 10061.361 8990.405 11132.32 8423.475 11699.25
## 2005.9014 10039.769 8968.038 11111.50 8400.698 11678.84
## 2005.9041 10046.557 8974.052 11119.06 8406.303 11686.81
## 2005.9068 10037.986 8964.708 11111.26 8396.548 11679.42
## 2005.9096 10045.275 8971.223 11119.33 8402.655 11687.89
## 2005.9123 10030.917 8956.093 11105.74 8387.116 11674.72
## 2005.9151 10001.777 8926.182 11077.37 8356.796 11646.76
## 2005.9178 10022.099 8945.732 11098.47 8375.938 11668.26
## 2005.9205 10029.009 8951.871 11106.15 8381.669 11676.35
## 2005.9233 10047.419 8969.511 11125.33 8398.901 11695.94
## 2005.9260 10065.511 8986.833 11144.19 8415.816 11715.21
## 2005.9288 10066.752 8987.306 11146.20 8415.881 11717.62
## 2005.9315 10049.229 8969.014 11129.44 8397.182 11701.28
## 2005.9342 10082.606 9001.623 11163.59 8429.385 11735.83
## 2005.9370 10064.194 8982.443 11145.94 8409.799 11718.59
## 2005.9397 10064.438 8981.920 11146.96 8408.870 11720.01
## 2005.9425 10056.260 8972.976 11139.54 8399.520 11713.00
## 2005.9452 10069.058 8985.008 11153.11 8411.146 11726.97
## 2005.9479 10070.393 8985.578 11155.21 8411.311 11729.47
## 2005.9507 10066.078 8980.498 11151.66 8405.826 11726.33
## 2005.9534 10071.786 8985.442 11158.13 8410.366 11733.21
## 2005.9562 10066.063 8978.955 11153.17 8403.474 11728.65
## 2005.9589 10073.946 8986.075 11161.82 8410.190 11737.70
## 2005.9616 10073.379 8984.746 11162.01 8408.458 11738.30
## 2005.9644 10073.981 8984.585 11163.38 8407.894 11740.07
## 2005.9671 10077.150 8986.993 11167.31 8409.898 11744.40
## 2005.9699 10105.396 9014.478 11196.31 8436.981 11773.81
## 2005.9726 10117.362 9025.683 11209.04 8447.784 11786.94
## 2005.9753 10104.318 9011.879 11196.76 8433.577 11775.06
## 2005.9781 10079.751 8986.553 11172.95 8407.849 11751.65
## 2005.9808 10054.534 8960.577 11148.49 8381.471 11727.60
## 2005.9836 10039.199 8944.483 11133.91 8364.976 11713.42
## 2005.9863 10048.477 8953.003 11143.95 8373.095 11723.86
## 2005.9890 10052.697 8956.466 11148.93 8376.157 11729.24
## 2005.9918 10066.834 8969.846 11163.82 8389.136 11744.53
## 2005.9945 10069.695 8971.951 11167.44 8390.841 11748.55
## 2005.9973 10087.467 8988.968 11185.97 8407.457 11767.48
## 2006.0000 10064.366 8965.111 11163.62 8383.201 11745.53
## 2006.0027 10067.201 8967.191 11167.21 8384.882 11749.52
## 2006.0055 10075.013 8974.249 11175.78 8391.540 11758.49##NOTE: AIC = 32047.14 , BIC = 32064.22 , RMSE = 31.77912
Also, the headline of the plot below contains ETS(A,N,N) showing that the automated model characterized error of the “tsWSR_PK” SERIES as Additative (A), trend as None (A) and seasonality as None (N) which is equivalent to simple exponential model(ses) with only alpha parameter i.e level.
#Model 2 : ARIMA Model
#Changing to stationary set(AutoRegressive Moving Average) It is used for forecasting for both seasonal and non- seasonal level.
#Changing to stationary set
train.sta_Var10 <- diff(train9)
test.sta_Var10 <- diff(test9)#2.1 Auto Arima model without sesonality:
set.seed(301)
model_Var10 <- auto.arima(train.sta_Var10, seasonal = FALSE)
summary(model_Var10)## Series: train.sta_Var10
## ARIMA(3,0,2) with zero mean
##
## Coefficients:
## ar1 ar2 ar3 ma1 ma2
## 0.5810 -0.1244 -0.0149 -0.5463 -0.3725
## s.e. 0.1652 0.1546 0.0731 0.1636 0.1495
##
## sigma^2 estimated as 979.6: log likelihood=-10656.84
## AIC=21325.67 AICc=21325.71 BIC=21359.83
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -0.1180388 31.26308 22.40424 NaN Inf 0.6098413 0.001649569##NOTE: AIC = 21325.67 , BIC = 21359.83 , RMSE = 31.26308
tsdisplay(residuals(model_Var10), lag.max = 45, main = '(1,1,1) Model Residuals')
#2.2 Auto Arima model with sesonality:
set.seed(301)
model2_Var10 <- auto.arima(train.sta_Var10, seasonal= TRUE)
summary(model2_Var10)## Series: train.sta_Var10
## ARIMA(3,0,2) with zero mean
##
## Coefficients:
## ar1 ar2 ar3 ma1 ma2
## 0.5810 -0.1244 -0.0149 -0.5463 -0.3725
## s.e. 0.1652 0.1546 0.0731 0.1636 0.1495
##
## sigma^2 estimated as 979.6: log likelihood=-10656.84
## AIC=21325.67 AICc=21325.71 BIC=21359.83
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -0.1180388 31.26308 22.40424 NaN Inf 0.6098413 0.001649569##NOTE: AIC = 21325.67 , BIC = 21359.83 , RMSE = 31.26308
tsdisplay(residuals(model2_Var10), lag.max = 20, main = 'Seasonal Model Residuals')
NOTE: Above Graphs shows serious lags at 13, so modify model for p or q = 13
- Manual ARIMA:
Passing parameter order = (3,0,13) which means p(member of lags of a variable to be used as a predictor) = 3, d = 0(members of differences needed for stationarity) and q = 13 (moving average order - number of lagged forecasts error in the prediction equation)
set.seed(301)
model1_Var10 <- arima(train.sta_Var10, order = c(3,0,13))
summary(model1_Var10)##
## Call:
## arima(x = train.sta_Var10, order = c(3, 0, 13))
##
## Coefficients:
## ar1 ar2 ar3 ma1 ma2 ma3 ma4 ma5
## 0.9497 0.1457 -0.6680 -0.9163 -0.6572 0.8243 0.2687 -0.1887
## s.e. 0.1509 0.2476 0.1478 0.1516 0.2431 0.0766 0.0895 0.0411
## ma6 ma7 ma8 ma9 ma10 ma11 ma12 ma13
## -0.1856 -0.031 -0.0403 0.0080 0.0360 -0.0513 0.0410 -0.0296
## s.e. 0.0416 0.041 0.0381 0.0384 0.0402 0.0336 0.0363 0.0248
## intercept
## 0.0084
## s.e. 0.0910
##
## sigma^2 estimated as 966.6: log likelihood = -10644.79, aic = 21325.57
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -0.1717054 31.0898 22.29635 NaN Inf 0.6759088 0.0009877062##NOTE: AIC = 21325.57 , RMSE = 31.0898
tsdisplay(residuals(model1_Var10), lag.max = 20, main = 'Seasonal Model Residuals')
Note: It seems good fit.
Fit the observed with the predicted values for both models in the same plot.
#Plotting forecast for each model
par(mfrow = c(2,2))
fit_auto_train_Var10 %>% forecast(h=341) %>% autoplot() 
model1_Var10 %>% forecast(h=341) %>% autoplot() 
model2_Var10 %>% forecast(h=341) %>% autoplot() 
model_Var10 %>% forecast(h=341) %>% autoplot()
COMMENT:
1. The plots includes 80% to 95% confidence interval.
2. For ARIMA models it plots the forecast but because of the nature of autoregressive process of 3 lags i.e. AR3, these forecast stabilizes quite smoothly.
Plot and comment on the residuals of the fitted data for both models in the same plot.
Residual Plot - to confirm no problem with this model
par(mfrow= c(2,2))
hist(fit_auto_train_Var10$residuals,col = 'red',xlab = 'Error',main = 'Histogram Of Residuals',freq= FALSE)
lines(density(fit_auto_train_Var10$residuals))
hist(model_Var10$residuals,col = 'red',xlab = 'Error',main = 'Histogram Of Residuals',freq= FALSE)
lines(density(model_Var10$residuals))
hist(model1_Var10$residuals,col = 'red',xlab = 'Error',main = 'Histogram Of Residuals',freq= FALSE)
lines(density(model1_Var10$residuals))
hist(model2_Var10$residuals,col = 'red',xlab = 'Error',main = 'Histogram Of Residuals',freq= FALSE)
lines(density(model2_Var10$residuals))
OBSERVATION: The residuals for each model are normally distributed, which shows the good fit of the models. It is normally distrbuted.
Testing the autocorrelation and partial autocorrelation of the residuals (using the plots and Ljung-Box Q statistic) up to an appropriate lag *
- ACF & PACF PLOTS
par(mfrow = c(4,2))
acf(fit_auto_train_Var10$residuals, main = 'Correlogram')
pacf(fit_auto_train_Var10$residuals, main = 'Partial Corelogram')
acf(model_Var10$residuals, main = 'Correlogram')
pacf(model_Var10$residuals, main = 'Partial Corelogram')
acf(model1_Var10$residuals, main = 'Correlogram')
pacf(model1_Var10$residuals, main = 'Partial Corelogram')
acf(model2_Var10$residuals, main = 'Correlogram')
pacf(model2_Var10$residuals, main = 'Partial Corelogram')
NOTE:
1. Residuals are the difference between actaual and fitted values
2. These blue lines are signficance bounds
3. This graph shows us the autocorelations for insample forecast errors
4. Do not exceed these significance bounds for lags 1 to end
- Ljunx-Box Test to check the autocorelations of the residuals
HO: No serial correlation upto 20 lags (does not exhibit lack of fit of the model)
Ha: Serial corelation is present (the model exhibits lack of fit)
We reject the null hypothesis, if p value is less than 0.05. This test is generally done for ARIMA models
Box.test(model_Var10$residuals, lag =20, type = 'Ljung-Box')##
## Box-Ljung test
##
## data: model_Var10$residuals
## X-squared = 19.094, df = 20, p-value = 0.5157Box.test(model1_Var10$residuals, lag =20, type = 'Ljung-Box')##
## Box-Ljung test
##
## data: model1_Var10$residuals
## X-squared = 6.7111, df = 20, p-value = 0.9975Box.test(model2_Var10$residuals, lag =20, type = 'Ljung-Box')##
## Box-Ljung test
##
## data: model2_Var10$residuals
## X-squared = 19.094, df = 20, p-value = 0.5157OBSERVATIONS:
For above performed Ljunx-Box Test on ARIMA models, we can say that p-value is more than significance level 0.05, then there is not a statistical significance.
We conclude that there is a liitle evidence of non-zero auto-corelations in the insample forecast errors at lags 1 to 20.
So we fail to rejects the null hypothesis. Hence, we conclude that there is no serial auto corelation present between lags. Hence, the model seems to be good fit.
Test and comment on the normality of the residuals.
Here, further testing the normality by plotting Normal Q-Q plots. From below plots we observed that most of the datapoints lies on the line. Hence, we could conclude that our model produces residuals that are normal
par(mfrow = c(2,2))
qqnorm(fit_auto_train_Var10$residuals)
qqnorm(model_Var10$residuals)
qqnorm(model1_Var10$residuals)
qqnorm(model2_Var10$residuals)
Validating The Model by testing the model performance with Holdout set
Here, choosing RMSE as evaluation parameter. The lower RMSE indicates a more accurate forecast.
Below, is the comparison of model. We are fitting the model to test set which is the holdout set. And checking the accuracy using RMSE(Root mean square error) evaluation parameter.
accuracy(forecast(fit_auto_train_Var10), test9) ["Test set", "RMSE"]## [1] 157.3138#o/p - 157.3138
accuracy(forecast(model1_Var10), test.sta_Var10) ["Test set", "RMSE"]## [1] 35.2608#O/P - 35.2608
accuracy(forecast(model2_Var10), test.sta_Var10) ["Test set", "RMSE"]## [1] 35.00271#o/p - 35.00271
accuracy(forecast(model_Var10), test.sta_Var10) ["Test set", "RMSE"]## [1] 35.00271#O/P - 35.00271NOTE:- Here, the RMSE value is less of ARIMA models compared to exponential model.
The minimum RMSE is of model2_Var10
COMMENT ON BEST MODEL AND ITS PARAMETERS
We observed the best model to be ARIMA model i.e.“model2_Var10”.
summary(model2_Var10)## Series: train.sta_Var10
## ARIMA(3,0,2) with zero mean
##
## Coefficients:
## ar1 ar2 ar3 ma1 ma2
## 0.5810 -0.1244 -0.0149 -0.5463 -0.3725
## s.e. 0.1652 0.1546 0.0731 0.1636 0.1495
##
## sigma^2 estimated as 979.6: log likelihood=-10656.84
## AIC=21325.67 AICc=21325.71 BIC=21359.83
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -0.1180388 31.26308 22.40424 NaN Inf 0.6098413 0.001649569The best forecasted model is ARIMA(3,0,3) ,which means
p = 3
d = 0
q = 3
For the best model, 3 member of lag are used as a predictor. As we transformed the series to stationary so members of differences needed for stationarity is 0. 3 are the number of lagged forecasts errors used in the prediction equation.
AIC = 21325.67, RMSE = 31.26308 which is minimum as compared to other models.
11. Forecasting on SLP change from previous day(SLP_)
#Checking the attributes of time series
attributes(tsSLP_)## $tsp
## [1] 1998.00 2004.94 365.00
##
## $class
## [1] "ts"#Plotting the series
plot(tsSLP_, main = "SLP change from previous day ", col = "red")
From the plot, we observes that there is absence of trend and seems to have seasonlity.
Checking the statistics and visualising the missing data in the series:
#Visualising the distribution of missing data
plotNA.distribution(tsSLP_)
As we see there is the missing data which is missed at random, so locf and NOCB seems the good technique to implement here.
#Impute the missing values with “na_locf” function of “imputeTS package” and visualise the imputed values in the time series
tsSLP_.imp <- na_locf(tsSLP_)
plotNA.imputations(tsSLP_, tsSLP_.imp)
#Decomposition Of Time Series
decomp10 <- decompose(tsSLP_.imp)
plot(decomp10, col = "red")
OBSERVATIONS:
1)There does not seems to have trend.
2)We observe some seasonality in the series. Seasonality describes cyclical effects due to the time of the year.
Let’s explore this seasonality pattern by plotting the decomp$seasonal components such that y-axis represents Seasonality Index and x-axis has month
#Plotting the decomposed series
plot(decomp10$seasonal[1:365], type ='b', xlab = 'Years', ylab = 'Seasonality Index', col = 'blue', las = 2, main = "SEASONAL DATA")
OBSERVATIONS:
- The plot shows a strong and significant sea level presuure in winter and summer.
- Also, no increase in the transition seasons.
#Stationarity check of time series We could check the stationarity of time series by ADF and KPSS Tests:
- Augmented Dickey- Fuller(ADF) t-statistic test for unit root
If we fail to reject the null hypothesis, we can say that the series is non-stationary. This means that the series can be linear or difference stationary[5]
adf.test(tsSLP_.imp)## Warning in adf.test(tsSLP_.imp): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: tsSLP_.imp
## Dickey-Fuller = -17.313, Lag order = 13, p-value = 0.01
## alternative hypothesis: stationaryNOTE: p-value is smaller, hence stationary
- Kwiatkowski-Phillips-Schmidt-Shin (KPSS) for level or trend stationarity
KPSS is another test for checking the stationarity of a time series.The null and alternate hypothesis for the KPSS test are opposite that of the ADF test,
kpss.test(tsSLP_.imp, null="Trend")## Warning in kpss.test(tsSLP_.imp, null = "Trend"): p-value greater than printed
## p-value##
## KPSS Test for Trend Stationarity
##
## data: tsSLP_.imp
## KPSS Trend = 0.0077208, Truncation lag parameter = 8, p-value = 0.1NOTE: p-value is greater, hence stationary
Plotting ACF to check the auto-corelations
acf(tsSLP_.imp,lag.max = length(tsSLP_.imp),xlab = "lag #", ylab = 'ACF',main='Statiionary Check ')
NOTE: Here, we observe the data lies inside the blue-dotted lines means the significance level.
#CREATING MODELS AND FORECASTING: USING EXPONENTIAL SMOOTHING AND ARIMA TECHNIQUES FOR TIME SERIES FORECASTING
- TRAIN- TEST SET SPLIT
train10 <- window(tsSLP_.imp, end = c(2004, 3))
test10 <- window(tsSLP_.imp, start = c(2004, 4))#Model 1 : Auto Exponential Smoothening Model
set.seed(301)
fit_auto_train_Var11 <- forecast(train10)
summary(fit_auto_train_Var11)##
## Forecast method: STL + ETS(A,N,N)
##
## Model Information:
## ETS(A,N,N)
##
## Call:
## ets(y = na.interp(x), model = etsmodel, allow.multiplicative.trend = allow.multiplicative.trend)
##
## Smoothing parameters:
## alpha = 1e-04
##
## Initial states:
## l = -0.2717
##
## sigma: 31.3596
##
## AIC AICc BIC
## 31986.86 31986.87 32003.94
##
## Error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -0.008456595 31.34532 22.85666 NaN Inf 0.624497 0.197499
##
## Forecasts:
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 2004.0082 -14.944234224 -55.133205 25.24473648 -76.40796 46.51949
## 2004.0110 -20.043176814 -60.232148 20.14579410 -81.50690 41.42055
## 2004.0137 -6.809591320 -46.998562 33.37937979 -68.27332 54.65414
## 2004.0164 -32.354517174 -72.543488 7.83445414 -93.81824 29.10921
## 2004.0192 24.633695925 -15.555276 64.82266744 -36.83003 86.09742
## 2004.0219 23.466577311 -16.722394 63.65554903 -37.99715 84.93031
## 2004.0247 14.788979412 -25.399993 54.97795133 -46.67475 76.25271
## 2004.0274 -28.466481825 -68.655454 11.72249029 -89.93021 32.99725
## 2004.0301 -17.606309820 -57.795282 22.58266250 -79.07004 43.85742
## 2004.0329 14.978494988 -25.210478 55.16746751 -46.48523 76.44222
## 2004.0356 22.819189972 -17.369783 63.00816269 -38.64454 84.28292
## 2004.0384 -6.800083677 -46.989057 33.38888925 -68.26381 54.66365
## 2004.0411 -25.872324109 -66.061297 14.31664902 -87.33605 35.59141
## 2004.0438 -19.989243985 -60.178217 20.19972934 -81.45297 41.47449
## 2004.0466 15.220560738 -24.968413 55.40953426 -46.24317 76.68429
## 2004.0493 2.149633508 -38.039340 42.33860724 -59.31410 63.61336
## 2004.0521 28.905047653 -11.283926 69.09402158 -32.55868 90.36878
## 2004.0548 37.443407807 -2.745566 77.63238194 -24.02032 98.90714
## 2004.0575 -25.792471566 -65.981446 14.39650277 -87.25620 35.67126
## 2004.0603 12.136299392 -28.052675 52.32527393 -49.32743 73.60003
## 2004.0630 -6.503576024 -46.692551 33.68539871 -67.96731 54.96016
## 2004.0658 -42.344881444 -82.533856 -2.15590651 -103.80861 19.11885
## 2004.0685 4.339557856 -35.849417 44.52853299 -57.12418 65.80329
## 2004.0712 28.676059935 -11.512915 68.86503527 -32.78767 90.13979
## 2004.0740 -17.175299000 -57.364275 23.01367654 -78.63903 44.28844
## 2004.0767 -1.449675262 -41.638651 38.73930048 -62.91341 60.01406
## 2004.0795 22.022511257 -18.166465 62.21148720 -39.44122 83.48625
## 2004.0822 -23.024594976 -63.213571 17.16438117 -84.48833 38.43914
## 2004.0849 -43.723487120 -83.912463 -3.53451078 -105.18722 17.74025
## 2004.0877 24.649349995 -15.539627 64.83832654 -36.81439 86.11309
## 2004.0904 4.281529988 -35.907447 44.47050674 -57.18221 65.74527
## 2004.0932 6.693862215 -33.495115 46.88283916 -54.76987 68.15760
## 2004.0959 14.424905782 -25.764071 54.61388293 -47.03883 75.88864
## 2004.0986 2.955701661 -37.233276 43.14467901 -58.50804 64.41944
## 2004.1014 1.804911884 -38.384066 41.99388944 -59.65883 63.26865
## 2004.1041 -17.729592226 -57.918570 22.45938553 -79.19333 43.73415
## 2004.1068 -3.425587699 -43.614566 36.76339026 -64.88933 58.03815
## 2004.1096 -12.287705389 -52.476684 27.90127277 -73.75144 49.17603
## 2004.1123 -13.144025430 -53.333004 27.04495293 -74.60776 48.31971
## 2004.1151 -30.231154317 -70.420133 9.95782424 -91.69489 31.23258
## 2004.1178 -10.620067064 -50.809046 29.56891170 -72.08381 50.84367
## 2004.1205 29.807457521 -10.381521 69.99643648 -31.65628 91.27120
## 2004.1233 27.930378302 -12.258601 68.11935746 -33.53336 89.39412
## 2004.1260 -15.946130865 -56.135110 24.24284850 -77.40987 45.51761
## 2004.1288 -8.230754177 -48.419734 31.95822539 -69.69449 53.23299
## 2004.1315 -30.915365685 -71.104345 9.27361408 -92.37911 30.54837
## 2004.1342 2.299493601 -37.889486 42.48847357 -59.16425 63.76323
## 2004.1370 31.333387793 -8.855592 71.52236796 -30.13035 92.79713
## 2004.1397 24.797570069 -15.391410 64.98655044 -36.66617 86.26131
## 2004.1425 -19.251055970 -59.440037 20.93792460 -80.71480 42.21269
## 2004.1452 -12.401040702 -52.590021 27.78794007 -73.86478 49.06270
## 2004.1479 -19.955345295 -60.144326 20.23363568 -81.41909 41.50840
## 2004.1507 -41.661244932 -81.850226 -1.47226376 -103.12499 19.80250
## 2004.1534 12.771660600 -27.417321 52.96064198 -48.69208 74.23540
## 2004.1562 2.346785367 -37.842196 42.53576695 -59.11696 63.81053
## 2004.1589 -10.630875827 -50.819858 29.55810595 -72.09462 50.83287
## 2004.1616 20.761873796 -19.427108 60.95085578 -40.70187 82.22562
## 2004.1644 12.693208407 -27.495774 52.88219059 -48.77054 74.15695
## 2004.1671 -39.783954451 -79.972937 0.40502793 -101.24770 21.67979
## 2004.1699 0.125219691 -40.063763 40.31420228 -61.33853 61.58896
## 2004.1726 19.483471594 -20.705511 59.67245438 -41.98027 80.94722
## 2004.1753 4.036089848 -36.152893 44.22507284 -57.42766 65.49984
## 2004.1781 -30.292465859 -70.481449 9.89651733 -91.75621 31.17128
## 2004.1808 2.078989234 -38.109994 42.26797262 -59.38476 63.54274
## 2004.1836 34.672236691 -5.516747 74.86122028 -26.79151 96.13598
## 2004.1863 28.730869540 -11.458114 68.91985333 -32.73288 90.19462
## 2004.1890 1.164042646 -39.024941 41.35302664 -60.29970 62.62779
## 2004.1918 -26.004463469 -66.193448 14.18452073 -87.46821 35.45928
## 2004.1945 -7.378041996 -47.567026 32.81094240 -68.84179 54.08571
## 2004.1973 -2.900796230 -43.089781 37.28818837 -64.36454 58.56295
## 2004.2000 -2.858526386 -43.047511 37.33045841 -64.32227 58.60522
## 2004.2027 -32.512216400 -72.701201 7.67676860 -93.97596 28.95153
## 2004.2055 -45.220340630 -85.409326 -5.03135543 -106.68409 16.24341
## 2004.2082 7.382217533 -32.806768 47.57120294 -54.08153 68.84597
## 2004.2110 26.843974367 -13.345011 67.03295997 -34.61978 88.30772
## 2004.2137 18.662595375 -21.526390 58.85158118 -42.80115 80.12635
## 2004.2164 -17.725392548 -57.914379 22.46359346 -79.18914 43.73836
## 2004.2192 1.646948641 -38.542038 41.83593485 -59.81680 63.11070
## 2004.2219 37.725771774 -2.463215 77.91475818 -23.73798 99.18952
## 2004.2247 21.701605209 -18.487381 61.89059182 -39.76215 83.16536
## 2004.2274 -0.046163600 -40.235150 40.14282321 -61.50991 61.41759
## 2004.2301 -15.712653958 -55.901641 24.47633306 -77.17641 45.75110
## 2004.2329 -11.008156055 -51.197143 29.18083116 -72.47191 50.45560
## 2004.2356 13.548278587 -26.640709 53.73726600 -47.91547 75.01203
## 2004.2384 4.745708874 -35.443279 44.93469649 -56.71804 66.20946
## 2004.2411 -19.765347525 -59.954335 20.42364029 -81.22910 41.69841
## 2004.2438 4.037778863 -36.151209 44.22676688 -57.42597 65.50153
## 2004.2466 5.622008468 -34.566980 45.81099669 -55.84175 67.08576
## 2004.2493 -2.019117282 -42.208106 38.16987114 -63.48287 59.44464
## 2004.2521 -30.234103589 -70.423092 9.95488503 -91.69786 31.22965
## 2004.2548 -11.838404799 -52.027394 28.35058403 -73.30216 49.62535
## 2004.2575 20.566094177 -19.622895 60.75508320 -40.89766 82.02985
## 2004.2603 29.835355832 -10.353633 70.02434506 -31.62840 91.29911
## 2004.2630 -2.148655290 -42.337645 38.04033414 -63.61241 59.31510
## 2004.2658 -11.185791576 -51.374781 29.00319805 -72.64955 50.27796
## 2004.2685 -19.836195809 -60.025186 20.35279402 -81.29995 41.62756
## 2004.2712 0.418781954 -39.770208 40.60777199 -61.04497 61.88254
## 2004.2740 11.666211928 -28.522778 51.85520216 -49.79754 73.12997
## 2004.2767 -0.073430186 -40.262421 40.11556025 -61.53719 61.39033
## 2004.2795 36.644505799 -3.544485 76.83349644 -24.81925 98.10826
## 2004.2822 -3.517731394 -43.706722 36.67125944 -64.98149 57.94603
## 2004.2849 -14.133310024 -54.322301 26.05568101 -75.59707 47.33045
## 2004.2877 -3.573322897 -43.762314 36.61566834 -65.03708 57.89044
## 2004.2904 -0.515860914 -40.704852 39.67313053 -61.97962 60.94790
## 2004.2932 5.329225908 -34.859766 45.51821755 -56.13453 66.79298
## 2004.2959 -10.149432995 -50.338425 30.03955885 -71.61319 51.31433
## 2004.2986 -13.823662748 -54.012655 26.36532930 -75.28742 47.64010
## 2004.3014 8.446314707 -31.742678 48.63530695 -53.01744 69.91007
## 2004.3041 13.844330236 -26.344662 54.03332268 -47.61943 75.30809
## 2004.3068 3.791095595 -36.397897 43.98008824 -57.67266 65.25486
## 2004.3096 -12.459446645 -52.648439 27.72954621 -73.92321 49.00431
## 2004.3123 5.684866444 -34.504127 45.87385950 -55.77889 67.14863
## 2004.3151 1.027257069 -39.161736 41.21625032 -60.43650 62.49102
## 2004.3178 -10.470796068 -50.659790 29.71819739 -71.93456 50.99297
## 2004.3205 2.538472225 -37.650521 42.72746588 -58.92529 64.00223
## 2004.3233 1.904192248 -38.284802 42.09318611 -59.55957 63.36795
## 2004.3260 -5.038257764 -45.227252 35.15073629 -66.50202 56.42550
## 2004.3288 8.294144969 -31.894849 48.48313923 -53.16962 69.75791
## 2004.3315 23.526178635 -16.662816 63.71517310 -37.93758 84.98994
## 2004.3342 2.893860553 -37.295134 43.08285522 -58.56990 64.35762
## 2004.3370 -14.869379033 -55.058374 25.31961583 -76.33314 46.59438
## 2004.3397 -21.294848694 -61.483844 18.89414637 -82.75861 40.16892
## 2004.3425 -2.922297359 -43.111293 37.26669791 -64.38606 58.54147
## 2004.3452 19.434507460 -20.754488 59.62350293 -42.02926 80.89827
## 2004.3479 -10.286921224 -50.475917 29.90207444 -71.75069 51.17684
## 2004.3507 -17.516077712 -57.705074 22.67291816 -78.97984 43.94769
## 2004.3534 4.590598236 -35.598398 44.77959431 -56.87317 66.05436
## 2004.3562 6.062425054 -34.126571 46.25142133 -55.40134 67.52619
## 2004.3589 -11.299568257 -51.488565 28.88942822 -72.76333 50.16420
## 2004.3616 -4.931292892 -45.120290 35.25770378 -66.39506 56.53247
## 2004.3644 10.999965659 -29.189031 51.18896254 -50.46380 72.46373
## 2004.3671 8.745706509 -31.443291 48.93470359 -52.71806 70.20947
## 2004.3699 4.763507401 -35.425490 44.95250468 -56.70026 66.22727
## 2004.3726 -4.202190244 -44.391188 35.98680724 -65.66596 57.26158
## 2004.3753 -0.649345017 -40.838343 39.53965266 -62.11311 60.81442
## 2004.3781 3.370809294 -36.818189 43.55980718 -58.09296 64.83458
## 2004.3808 11.633735944 -28.555262 51.82273403 -49.83003 73.09750
## 2004.3836 -7.199646116 -47.388644 32.98935217 -68.66341 54.26412
## 2004.3863 -6.187807773 -46.376806 34.00119071 -67.65158 55.27596
## 2004.3890 -6.551566742 -46.740565 33.63743195 -68.01534 54.91220
## 2004.3918 8.686917821 -31.502081 48.87591671 -52.77685 70.15069
## 2004.3945 3.947583503 -36.241416 44.13658259 -57.51619 65.41135
## 2004.3973 1.214615833 -38.974383 41.40361513 -60.24915 62.67839
## 2004.4000 -1.062335916 -41.251335 39.12666358 -62.52611 60.40143
## 2004.4027 -1.870528889 -42.059529 38.31847081 -63.33430 59.59324
## 2004.4055 -5.313753388 -45.502753 34.87524651 -66.77752 56.15002
## 2004.4082 1.686078435 -38.502922 41.87507853 -59.77769 63.14985
## 2004.4110 6.732946270 -33.456054 46.92194657 -54.73083 68.19672
## 2004.4137 -4.712038561 -44.901039 35.47696194 -66.17581 56.75173
## 2004.4164 -3.321199016 -43.510200 36.86780169 -64.78497 58.14257
## 2004.4192 11.739433482 -28.449567 51.92843438 -49.72434 73.20321
## 2004.4219 2.369557402 -37.819444 42.55855851 -59.09422 63.83333
## 2004.4247 -2.344310137 -42.533311 37.84469117 -63.80808 59.11946
## 2004.4274 -4.828056199 -45.017058 35.36094531 -66.29183 56.63572
## 2004.4301 3.804976526 -36.384025 43.99397823 -57.65880 65.26875
## 2004.4329 15.258119311 -24.930883 55.44712122 -46.20566 76.72189
## 2004.4356 4.041047614 -36.147954 44.23004972 -57.42273 65.50482
## 2004.4384 -20.267566373 -60.456569 19.92143594 -81.73134 41.19621
## 2004.4411 -7.155687836 -47.344690 33.03331468 -68.61946 54.30809
## 2004.4438 1.895808570 -38.293194 42.08481128 -59.56797 63.35958
## 2004.4466 12.439120205 -27.749883 52.62812312 -49.02466 73.90290
## 2004.4493 4.917837084 -35.271166 45.10684020 -56.54594 66.38161
## 2004.4521 4.752437341 -35.436566 44.94144066 -56.71134 66.21621
## 2004.4548 -0.918585749 -41.107589 39.27041777 -62.38236 60.54519
## 2004.4575 0.890125652 -39.298878 41.07912937 -60.57365 62.35390
## 2004.4603 0.788916716 -39.400087 40.97792064 -60.67486 62.25269
## 2004.4630 -2.224609855 -42.413614 37.96439427 -63.68839 59.23917
## 2004.4658 0.195491553 -39.993513 40.38449588 -61.26829 61.65927
## 2004.4685 10.283187554 -29.905817 50.47219208 -51.18059 71.74697
## 2004.4712 -0.590986679 -40.779991 39.59801805 -62.05477 60.87279
## 2004.4740 -4.062571494 -44.251576 36.12643343 -65.52635 57.40121
## 2004.4767 -0.740515476 -40.929521 39.44848965 -62.20429 60.72326
## 2004.4795 10.785741737 -29.403264 50.97474707 -50.67804 72.24952
## 2004.4822 6.895598254 -33.293407 47.08460379 -54.56818 68.35938
## 2004.4849 -7.876892225 -48.065898 32.31211351 -69.34067 53.58689
## 2004.4877 -8.378733784 -48.567740 31.81027215 -69.84251 53.08505
## 2004.4904 -6.135640188 -46.324646 34.05336595 -67.59942 55.32814
## 2004.4932 -3.140599854 -43.329606 37.04840648 -64.60438 58.32318
## 2004.4959 4.872664912 -35.316342 45.06167145 -56.59112 66.33645
## 2004.4986 0.471194505 -39.717812 40.66020125 -60.99259 61.93498
## 2004.5014 1.819876977 -38.369130 42.00888392 -59.64391 63.28366
## 2004.5041 0.260866590 -39.928141 40.44987373 -61.20292 61.72465
## 2004.5068 0.652872013 -39.536135 40.84187936 -60.81091 62.11665
## 2004.5096 3.158157520 -37.030850 43.34716506 -58.30563 64.62194
## 2004.5123 -4.899607996 -45.088616 35.28939975 -66.36339 56.56418
## 2004.5151 -14.255848780 -54.444857 25.93315917 -75.71963 47.20793
## 2004.5178 -5.346161444 -45.535170 34.84284671 -66.80995 56.11762
## 2004.5205 -0.130601655 -40.319610 40.05840670 -61.59439 61.33318
## 2004.5233 -1.429946630 -41.618955 38.75906192 -62.89373 60.03384
## 2004.5260 -3.520436698 -43.709445 36.66857206 -64.98422 57.94335
## 2004.5288 -4.423084011 -44.612093 35.76592494 -65.88687 57.04070
## 2004.5315 6.860193016 -33.328816 47.04920217 -54.60359 68.32398
## 2004.5342 12.305945063 -27.883064 52.49495442 -49.15784 73.76973
## 2004.5370 8.377967953 -31.811042 48.56697751 -53.08582 69.84175
## 2004.5397 -9.578199522 -49.767209 30.61081024 -71.04199 51.88559
## 2004.5425 -11.869938832 -52.058949 28.31907113 -73.33373 49.59385
## 2004.5452 -6.124843841 -46.313854 34.06416632 -67.58863 55.33894
## 2004.5479 5.153006412 -35.036004 45.34201678 -56.31078 66.61679
## 2004.5507 5.680054223 -34.508956 45.86906479 -55.78373 67.14384
## 2004.5534 -8.809371753 -48.998383 31.37963901 -70.27316 52.65442
## 2004.5562 -8.043412560 -48.232424 32.14559841 -69.50720 53.42038
## 2004.5589 6.938560688 -33.250450 47.12757186 -54.52523 68.40235
## 2004.5616 0.317952259 -39.871059 40.50696363 -61.14584 61.78174
## 2004.5644 0.589263475 -39.599748 40.77827505 -60.87453 62.05305
## 2004.5671 0.040700618 -40.148311 40.22971239 -61.42309 61.50449
## 2004.5699 -1.392503849 -41.581516 38.79650812 -62.85629 60.07129
## 2004.5726 -10.096538067 -50.285550 30.09247411 -71.56033 51.36725
## 2004.5753 1.172272123 -39.016740 41.36128450 -60.29152 62.63606
## 2004.5781 3.011391289 -37.177621 43.20040387 -58.45240 64.47518
## 2004.5808 -5.249462129 -45.438475 34.93955065 -66.71325 56.21433
## 2004.5836 -0.009372358 -40.198385 40.17964062 -61.47316 61.45442
## 2004.5863 9.973797669 -30.215216 50.16281085 -51.48999 71.43759
## 2004.5890 11.337201906 -28.851811 51.52621529 -50.12659 72.80099
## 2004.5918 1.363517866 -38.825496 41.55253145 -60.10027 62.82731
## 2004.5945 -6.679088233 -46.868102 33.50992555 -68.14288 54.78470
## 2004.5973 -10.078155251 -50.267169 30.11085874 -71.54195 51.38564
## 2004.6000 -3.494046882 -43.683061 36.69496731 -64.95784 57.96975
## 2004.6027 0.365457595 -39.823557 40.55447198 -61.09834 61.82925
## 2004.6055 1.321938136 -38.867076 41.51095273 -60.14186 62.78573
## 2004.6082 0.259100699 -39.929914 40.44811549 -61.20469 61.72289
## 2004.6110 5.211858549 -34.977156 45.40087354 -56.25194 66.67565
## 2004.6137 0.230382593 -39.958633 40.41939779 -61.23341 61.69418
## 2004.6164 -11.280004609 -51.469020 28.90901079 -72.74380 50.18379
## 2004.6192 -9.558929989 -49.747946 30.63008561 -71.02273 51.90487
## 2004.6219 8.960930222 -31.228086 49.14994602 -52.50287 70.42473
## 2004.6247 -0.781462540 -40.970479 39.40755346 -62.24526 60.68233
## 2004.6274 -10.276035813 -50.465052 29.91298039 -71.73983 51.18776
## 2004.6301 -14.015221099 -54.204238 26.17379530 -75.47902 47.44858
## 2004.6329 7.102783580 -33.086233 47.29180018 -54.36101 68.56658
## 2004.6356 4.806113672 -35.382903 44.99513048 -56.65768 66.26991
## 2004.6384 -16.413671966 -56.602689 23.77534504 -77.87747 45.05013
## 2004.6411 -0.714025543 -40.903043 39.47499166 -62.17782 60.74977
## 2004.6438 16.152691648 -24.036326 56.34170906 -45.31111 77.61649
## 2004.6466 10.212896722 -29.976121 50.40191433 -51.25090 71.67670
## 2004.6493 -6.692916168 -46.881934 33.49610164 -68.15671 54.77088
## 2004.6521 -3.369177506 -43.558196 36.81984051 -64.83298 58.09462
## 2004.6548 1.636830061 -38.552188 41.82584828 -59.82697 63.10063
## 2004.6575 12.876453072 -27.312565 53.06547149 -48.58735 74.34025
## 2004.6603 3.065502726 -37.123516 43.25452134 -58.39830 64.52930
## 2004.6630 -11.041156105 -51.230175 29.14786271 -72.50496 50.42264
## 2004.6658 -6.676852735 -46.865872 33.51216628 -68.14065 54.78695
## 2004.6685 15.775552886 -24.413466 55.96457211 -45.68825 77.23935
## 2004.6712 -6.437295515 -46.626315 33.75172391 -67.90110 55.02651
## 2004.6740 -4.519579817 -44.708599 35.66943981 -65.98338 56.94422
## 2004.6767 -0.550572890 -40.739593 39.63844693 -62.01437 60.91323
## 2004.6795 -13.364800765 -53.553821 26.82421926 -74.82860 48.09900
## 2004.6822 -23.695929400 -63.884950 16.49309083 -85.15973 37.76787
## 2004.6849 14.651046788 -25.537974 54.84006722 -46.81276 76.11485
## 2004.6877 25.348432274 -14.840588 65.53745290 -36.11537 86.81224
## 2004.6904 11.883488878 -28.305532 52.07250971 -49.58031 73.34729
## 2004.6932 -0.444430854 -40.633452 39.74459018 -61.90823 61.01937
## 2004.6959 -3.640901748 -43.829923 36.54811948 -65.10471 57.82290
## 2004.6986 -7.302176963 -47.491198 32.88684447 -68.76598 54.16163
## 2004.7014 -3.641106308 -43.830128 36.54791533 -65.10491 57.82270
## 2004.7041 -2.972993469 -43.162015 37.21602837 -64.43680 58.49081
## 2004.7068 -6.482059185 -46.671081 33.70696285 -67.94586 54.98175
## 2004.7096 3.197266485 -36.991756 43.38628872 -58.26654 64.66107
## 2004.7123 4.045585404 -36.143437 44.23460785 -57.41822 65.50939
## 2004.7151 -15.747323203 -55.936346 24.44169944 -77.21113 45.71648
## 2004.7178 -0.359501137 -40.548524 39.82952171 -61.82331 61.10431
## 2004.7205 14.939584253 -25.249439 55.12860730 -46.52422 76.40339
## 2004.7233 -0.420247627 -40.609271 39.76877562 -61.88405 61.04356
## 2004.7260 -4.405194451 -44.594218 35.78382900 -65.86900 57.05861
## 2004.7288 -7.162702058 -47.351726 33.02632159 -68.62651 54.30111
## 2004.7315 29.473710313 -10.715314 69.66273416 -31.99010 90.93752
## 2004.7342 7.289043929 -32.899980 47.47806798 -54.17476 68.75285
## 2004.7370 14.753126927 -25.435897 54.94215118 -46.71068 76.21694
## 2004.7397 -11.318599800 -51.507624 28.87042465 -72.78241 50.14521
## 2004.7425 -8.433247773 -48.622272 31.75577688 -69.89706 53.03056
## 2004.7452 -5.549215673 -45.738241 34.63980918 -67.01303 55.91459
## 2004.7479 -23.085363008 -63.274388 17.10366205 -84.54917 38.37845
## 2004.7507 2.687074838 -37.501950 42.87610010 -58.77674 64.15088
## 2004.7534 10.355443743 -29.833582 50.54446920 -51.10837 71.81925
## 2004.7562 6.474768021 -33.714258 46.66379368 -54.98904 67.93858
## 2004.7589 9.017072063 -31.171954 49.20609793 -52.44674 70.48088
## 2004.7616 -0.313049178 -40.502075 39.87597689 -61.77686 61.15076
## 2004.7644 -18.192051078 -58.381077 21.99697519 -79.65586 43.27176
## 2004.7671 -4.668004332 -44.857031 35.52102213 -66.13182 56.79581
## 2004.7699 4.242212012 -35.946815 44.43123868 -57.22160 65.70602
## 2004.7726 13.326952157 -26.862075 53.51597903 -48.13686 74.79076
## 2004.7753 11.868349688 -28.320677 52.05737676 -49.59546 73.33216
## 2004.7781 10.038751220 -30.150276 50.22777849 -51.42506 71.50256
## 2004.7808 -6.022435168 -46.211463 34.16659231 -67.48625 55.44138
## 2004.7836 -1.493373840 -41.682402 38.69565383 -62.95719 59.97044
## 2004.7863 -3.863657776 -44.052686 36.32537010 -65.32747 57.60016
## 2004.7890 28.491806026 -11.697222 68.68083410 -32.97201 89.95562
## 2004.7918 23.366433533 -16.822595 63.55546181 -38.09738 84.83025
## 2004.7945 -2.025033965 -42.214062 38.16399451 -63.48885 59.43878
## 2004.7973 -10.115874669 -50.304903 30.07315401 -71.57969 51.34794
## 2004.8000 -22.120572462 -62.309601 18.06845642 -83.58439 39.34324
## 2004.8027 -18.633097093 -58.822126 21.55593199 -80.09691 42.83072
## 2004.8055 11.472170479 -28.716859 51.66119976 -49.99165 72.93599
## 2004.8082 -4.452967296 -44.641997 35.73606219 -65.91678 57.01085
## 2004.8110 -2.088101534 -42.277131 38.10092815 -63.55192 59.37572
## 2004.8137 -30.804157815 -70.993188 9.38487207 -92.26798 30.65966
## 2004.8164 7.067409895 -33.121620 47.25643998 -54.39641 68.53123
## 2004.8192 3.712546384 -36.476484 43.90157668 -57.75127 65.17636
## 2004.8219 7.572529095 -32.616501 47.76155959 -53.89129 69.03635
## 2004.8247 28.150278060 -12.038753 68.33930875 -33.31354 89.61410
## 2004.8274 -15.603545637 -55.792577 24.58548526 -77.06736 45.86027
## 2004.8301 -16.207408604 -56.396440 23.98162249 -77.67123 45.25641
## 2004.8329 -10.645241814 -50.834273 29.54378948 -72.10906 50.81858
## 2004.8356 35.710018195 -4.479013 75.89904969 -25.75380 97.17384
## 2004.8384 3.689909279 -36.499122 43.87894098 -57.77391 65.15373
## 2004.8411 -35.408441562 -75.597473 4.78059034 -96.87226 26.05538
## 2004.8438 11.358040410 -28.830992 51.54707251 -50.10578 72.82186
## 2004.8466 38.429973769 -1.759059 78.61900607 -23.03385 99.89379
## 2004.8493 24.063058391 -16.125974 64.25209090 -37.40076 85.52688
## 2004.8521 -5.787126206 -45.976159 34.40190650 -67.25095 55.67670
## 2004.8548 -22.784474795 -62.973508 17.40455811 -84.24830 38.67935
## 2004.8575 -1.968019962 -42.157053 38.22101315 -63.43184 59.49580
## 2004.8603 -37.829400588 -78.018434 2.35963272 -99.29322 23.63442
## 2004.8630 -40.123969149 -80.313003 0.06506436 -101.58779 21.33985
## 2004.8658 20.501802312 -19.687231 60.69083603 -40.96202 81.96563
## 2004.8685 35.038623064 -5.150411 75.22765698 -26.42520 96.50245
## 2004.8712 13.309700314 -26.879334 53.49873443 -48.15412 74.77352
## 2004.8740 -4.899793566 -45.088828 35.28924075 -66.36362 56.56403
## 2004.8767 -10.019477766 -50.208512 30.16955675 -71.48330 51.44435
## 2004.8795 24.652504530 -15.536530 64.84153925 -36.81132 86.11633
## 2004.8822 4.821624372 -35.367411 45.01065929 -56.64220 66.28545
## 2004.8849 -4.247618128 -44.436653 35.94141699 -65.71144 57.21621
## 2004.8877 -12.995706907 -53.184742 27.19332842 -74.45953 48.46812
## 2004.8904 -2.966753841 -43.155789 37.22228168 -64.43058 58.49707
## 2004.8932 16.489091830 -23.699944 56.67812756 -44.97473 77.95292
## 2004.8959 -8.341499713 -48.530536 31.84753622 -69.80533 53.12233
## 2004.8986 6.585693797 -33.603342 46.77472993 -54.87813 68.04952
## 2004.9014 -21.514480942 -61.703517 18.67455539 -82.97831 39.94935
## 2004.9041 6.866791027 -33.322246 47.05582756 -54.59704 68.33062
## 2004.9068 -8.491147167 -48.680184 31.69788957 -69.95497 52.97268
## 2004.9096 7.366899570 -32.822137 47.55593650 -54.09693 68.83073
## 2004.9123 -14.278205782 -54.467243 25.91083135 -75.74203 47.18562
## 2004.9151 -29.059196359 -69.248234 11.12984098 -90.52302 32.40463
## 2004.9178 20.403320040 -19.785717 60.59235758 -41.06051 81.86715
## 2004.9205 6.991772363 -33.197265 47.18081010 -54.47206 68.45560
## 2004.9233 18.493458337 -21.695580 58.68249628 -42.97037 79.95729
## 2004.9260 18.176142134 -22.012896 58.36518028 -43.28769 79.63997
## 2004.9288 12.451507815 -27.737531 52.64054616 -49.01232 73.91534
## 2004.9315 1.251708469 -38.937330 41.44074701 -60.21212 62.71554
## 2004.9342 33.475024666 -6.714014 73.66406341 -27.98881 94.93886
## 2004.9370 -18.313315940 -58.502355 21.87572301 -79.77715 43.15052
## 2004.9397 -4.757711441 -44.946751 35.43132771 -66.22154 56.70612
## 2004.9425 -2.387925109 -42.576964 37.80111424 -63.85176 59.07591
## 2004.9452 15.986501530 -24.202538 56.17554108 -45.47733 77.45033
## 2004.9479 1.441643683 -38.747396 41.63068343 -60.02219 62.90548
## 2004.9507 -4.207474292 -44.396514 35.98156566 -65.67131 57.25636
## 2004.9534 5.818011203 -34.371029 46.00705136 -55.64582 67.28184
## 2004.9562 -5.612617543 -45.801658 34.57642281 -67.07645 55.85122
## 2004.9589 7.995900077 -32.193140 48.18494063 -53.46793 69.45973
## 2004.9616 0.870249733 -39.318791 41.05929049 -60.59358 62.33408
## 2004.9644 -1.485733515 -41.674774 38.70330744 -62.94957 59.97810
## 2004.9671 4.522164280 -35.666877 44.71120544 -56.94167 65.98600
## 2004.9699 20.927021402 -19.262020 61.11606276 -40.53681 82.39086
## 2004.9726 10.719934566 -29.469107 50.90897613 -50.74390 72.18377
## 2004.9753 -17.023367657 -57.212409 23.16567411 -78.48720 44.44047
## 2004.9781 -28.848344045 -69.037386 11.34069792 -90.31218 32.61549
## 2004.9808 -32.141652930 -72.330695 8.04738924 -93.60549 29.32218
## 2004.9836 -15.207289173 -55.396332 24.98175320 -76.67113 46.25655
## 2004.9863 2.797376773 -37.391666 42.98641934 -58.66646 64.26121
## 2004.9890 4.351510375 -35.837532 44.54055315 -57.11233 65.81535
## 2004.9918 14.270432014 -25.918611 54.45947499 -47.19341 75.73427
## 2004.9945 -2.076693282 -42.265736 38.11234989 -63.54053 59.38714
## 2004.9973 12.836645857 -27.352398 53.02568923 -48.62719 74.30048
## 2005.0000 -16.715050963 -56.904095 23.47399261 -78.17889 44.74879
## 2005.0027 3.020884290 -37.168159 43.20992807 -58.44295 64.48472
## 2005.0055 7.999234299 -32.189810 48.18827828 -53.46460 69.46307
## 2005.0082 -14.944234224 -55.133278 25.24480996 -76.40807 46.51960
## 2005.0110 -20.043176814 -60.232221 20.14586757 -81.50702 41.42066
## 2005.0137 -6.809591320 -46.998636 33.37945326 -68.27343 54.65425
## 2005.0164 -32.354517174 -72.543562 7.83452761 -93.81836 29.10932
## 2005.0192 24.633695925 -15.555349 64.82274091 -36.83014 86.09754
## 2005.0219 23.466577311 -16.722468 63.65562250 -37.99726 84.93042
## 2005.0247 14.788979412 -25.400066 54.97802480 -46.67486 76.25282
## 2005.0274 -28.466481825 -68.655527 11.72256376 -89.93032 32.99736
## 2005.0301 -17.606309820 -57.795356 22.58273597 -79.07015 43.85753
## 2005.0329 14.978494988 -25.210551 55.16754098 -46.48535 76.44234
## 2005.0356 22.819189972 -17.369856 63.00823617 -38.64465 84.28303
## 2005.0384 -6.800083677 -46.989130 33.38896272 -68.26393 54.66376
## 2005.0411 -25.872324109 -66.061371 14.31672249 -87.33617 35.59152
## 2005.0438 -19.989243985 -60.178291 20.19980281 -81.45309 41.47460
## 2005.0466 15.220560738 -24.968486 55.40960774 -46.24328 76.68440
## 2005.0493 2.149633508 -38.039414 42.33868071 -59.31421 63.61348
## 2005.0521 28.905047653 -11.284000 69.09409505 -32.55880 90.36889
## 2005.0548 37.443407807 -2.745640 77.63245541 -24.02044 98.90725
## 2005.0575 -25.792471566 -65.981519 14.39657624 -87.25632 35.67137
## 2005.0603 12.136299392 -28.052749 52.32534740 -49.32755 73.60014
## 2005.0630 -6.503576024 -46.692624 33.68547218 -67.96742 54.96027
## 2005.0658 -42.344881444 -82.533930 -2.15583304 -103.80873 19.11896
## 2005.0685 4.339557856 -35.849491 44.52860647 -57.12429 65.80340
## 2005.0712 28.676059935 -11.512989 68.86510875 -32.78779 90.13991
## 2005.0740 -17.175299000 -57.364348 23.01375001 -78.63915 44.28855
## 2005.0767 -1.449675262 -41.638724 38.73937395 -62.91352 60.01417
## 2005.0795 22.022511257 -18.166538 62.21156067 -39.44134 83.48636
## 2005.0822 -23.024594976 -63.213645 17.16445464 -84.48844 38.43925
## 2005.0849 -43.723487120 -83.912537 -3.53443730 -105.18733 17.74036
## 2005.0877 24.649349995 -15.539700 64.83840001 -36.81450 86.11320
## 2005.0904 4.281529988 -35.907520 44.47058021 -57.18232 65.74538
## 2005.0932 6.693862215 -33.495188 46.88291264 -54.76999 68.15771
## 2005.0959 14.424905782 -25.764145 54.61395640 -47.03894 75.88875
## 2005.0986 2.955701661 -37.233349 43.14475248 -58.50815 64.41955
## 2005.1014 1.804911884 -38.384139 41.99396291 -59.65894 63.26876
## 2005.1041 -17.729592226 -57.918643 22.45945900 -79.19344 43.73426
## 2005.1068 -3.425587699 -43.614639 36.76346373 -64.88944 58.03826
## 2005.1096 -12.287705389 -52.476757 27.90134624 -73.75156 49.17615
## 2005.1123 -13.144025430 -53.333077 27.04502640 -74.60788 48.31983
## 2005.1151 -30.231154317 -70.420206 9.95789771 -91.69501 31.23270
## 2005.1178 -10.620067064 -50.809119 29.56898517 -72.08392 50.84378
## 2005.1205 29.807457521 -10.381595 69.99650995 -31.65639 91.27131
## 2005.1233 27.930378302 -12.258674 68.11943094 -33.53347 89.39423
## 2005.1260 -15.946130865 -56.135184 24.24292197 -77.40998 45.51772
## 2005.1288 -8.230754177 -48.419807 31.95829886 -69.69461 53.23310
## 2005.1315 -30.915365685 -71.104419 9.27368755 -92.37922 30.54849
## 2005.1342 2.299493601 -37.889560 42.48854704 -59.16436 63.76335
## 2005.1370 31.333387793 -8.855666 71.52244143 -30.13047 92.79724
## 2005.1397 24.797570069 -15.391484 64.98662391 -36.66628 86.26142
## 2005.1425 -19.251055970 -59.440110 20.93799807 -80.71491 42.21280
## 2005.1452 -12.401040702 -52.590095 27.78801354 -73.86490 49.06281
## 2005.1479 -19.955345295 -60.144400 20.23370915 -81.41920 41.50851
## 2005.1507 -41.661244932 -81.850300 -1.47219028 -103.12510 19.80261
## 2005.1534 12.771660600 -27.417394 52.96071545 -48.69219 74.23552
## 2005.1562 2.346785367 -37.842270 42.53584042 -59.11707 63.81064
## 2005.1589 -10.630875827 -50.819931 29.55817942 -72.09473 50.83298
## 2005.1616 20.761873796 -19.427182 60.95092925 -40.70198 82.22573
## 2005.1644 12.693208407 -27.495847 52.88226406 -48.77065 74.15707
## 2005.1671 -39.783954451 -79.973010 0.40510140 -101.24781 21.67990
## 2005.1699 0.125219691 -40.063836 40.31427575 -61.33864 61.58908
## 2005.1726 19.483471594 -20.705585 59.67252785 -41.98039 80.94733
## 2005.1753 4.036089848 -36.152967 44.22514631 -57.42777 65.49995
## 2005.1781 -30.292465859 -70.481523 9.89659080 -91.75632 31.17139
## 2005.1808 2.078989234 -38.110068 42.26804610 -59.38487 63.54285
## 2005.1836 34.672236691 -5.516820 74.86129375 -26.79162 96.13610
## 2005.1863 28.730869540 -11.458188 68.91992680 -32.73299 90.19473
## 2005.1890 1.164042646 -39.025015 41.35310011 -60.29982 62.62790
## 2005.1918 -26.004463469 -66.193521 14.18459420 -87.46832 35.45940
## 2005.1945 -7.378041996 -47.567100 32.81101587 -68.84190 54.08582
## 2005.1973 -2.900796230 -43.089854 37.28826184 -64.36466 58.56306
## 2005.2000 -2.858526386 -43.047585 37.33053189 -64.32239 58.60533
## 2005.2027 -32.512216400 -72.701275 7.67684207 -93.97608 28.95164
## 2005.2055 -45.220340630 -85.409399 -5.03128196 -106.68420 16.24352
## 2005.2082 7.382217533 -32.806841 47.57127641 -54.08164 68.84608
## 2005.2110 26.843974367 -13.345085 67.03303344 -34.61989 88.30784
## 2005.2137 18.662595375 -21.526464 58.85165465 -42.80127 80.12646
## 2005.2164 -17.725392548 -57.914452 22.46366693 -79.18926 43.73847
## 2005.2192 1.646948641 -38.542111 41.83600832 -59.81691 63.11081
## 2005.2219 37.725771774 -2.463288 77.91483166 -23.73809 99.18963
## 2005.2247 21.701605209 -18.487455 61.89066529 -39.76226 83.16547
## 2005.2274 -0.046163600 -40.235224 40.14289668 -61.51003 61.41770
## 2005.2301 -15.712653958 -55.901714 24.47640653 -77.17652 45.75121
## 2005.2329 -11.008156055 -51.197217 29.18090463 -72.47202 50.45571
## 2005.2356 13.548278587 -26.640782 53.73733947 -47.91559 75.01214
## 2005.2384 4.745708874 -35.443352 44.93476996 -56.71816 66.20957
## 2005.2411 -19.765347525 -59.954409 20.42371377 -81.22921 41.69852
## 2005.2438 4.037778863 -36.151283 44.22684035 -57.42609 65.50164
## 2005.2466 5.622008468 -34.567053 45.81107016 -55.84186 67.08587
## 2005.2493 -2.019117282 -42.208179 38.16994461 -63.48298 59.44475
## 2005.2521 -30.234103589 -70.423166 9.95495851 -91.69797 31.22976
## 2005.2548 -11.838404799 -52.027467 28.35065750 -73.30227 49.62546
## 2005.2575 20.566094177 -19.622968 60.75515668 -40.89777 82.02996
## 2005.2603 29.835355832 -10.353707 70.02441853 -31.62851 91.29922
## 2005.2630 -2.148655290 -42.337718 38.04040761 -63.61252 59.31521
## 2005.2658 -11.185791576 -51.374855 29.00327153 -72.64966 50.27808
## 2005.2685 -19.836195809 -60.025259 20.35286749 -81.30006 41.62767
## 2005.2712 0.418781954 -39.770282 40.60784546 -61.04509 61.88265
## 2005.2740 11.666211928 -28.522852 51.85527563 -49.79766 73.13008
## 2005.2767 -0.073430186 -40.262494 40.11563372 -61.53730 61.39044
## 2005.2795 36.644505799 -3.544558 76.83356991 -24.81936 98.10838
## 2005.2822 -3.517731394 -43.706796 36.67133292 -64.98160 57.94614
## 2005.2849 -14.133310024 -54.322375 26.05575449 -75.59718 47.33056
## 2005.2877 -3.573322897 -43.762388 36.61574182 -65.03719 57.89055
## 2005.2904 -0.515860914 -40.704926 39.67320400 -61.97973 60.94801
## 2005.2932 5.329225908 -34.859839 45.51829102 -56.13465 66.79310
## 2005.2959 -10.149432995 -50.338498 30.03963232 -71.61330 51.31444
## 2005.2986 -13.823662748 -54.012728 26.36540277 -75.28753 47.64021
## 2005.3014 8.446314707 -31.742751 48.63538043 -53.01756 69.91019
## 2005.3041 13.844330236 -26.344736 54.03339616 -47.61954 75.30820
## 2005.3068 3.791095595 -36.397971 43.98016172 -57.67278 65.25497
## 2005.3096 -12.459446645 -52.648513 27.72961968 -73.92332 49.00443
## 2005.3123 5.684866444 -34.504200 45.87393297 -55.77901 67.14874
## 2005.3151 1.027257069 -39.161810 41.21632379 -60.43662 62.49113
## 2005.3178 -10.470796068 -50.659863 29.71827086 -71.93467 50.99308
## 2005.3205 2.538472225 -37.650595 42.72753935 -58.92540 64.00235
## 2005.3233 1.904192248 -38.284875 42.09325958 -59.55968 63.36807
## 2005.3260 -5.038257764 -45.227325 35.15080977 -66.50213 56.42562
## 2005.3288 8.294144969 -31.894923 48.48321270 -53.16973 69.75802
## 2005.3315 23.526178635 -16.662889 63.71524657 -37.93770 84.99005
## 2005.3342 2.893860553 -37.295208 43.08292869 -58.57002 64.35774
## 2005.3370 -14.869379033 -55.058447 25.31968930 -76.33326 46.59450
## 2005.3397 -21.294848694 -61.483917 18.89421984 -82.75873 40.16903
## 2005.3425 -2.922297359 -43.111366 37.26677138 -64.38617 58.54158
## 2005.3452 19.434507460 -20.754561 59.62357640 -42.02937 80.89838
## 2005.3479 -10.286921224 -50.475990 29.90214792 -71.75080 51.17696
## 2005.3507 -17.516077712 -57.705147 22.67299163 -78.97996 43.94780
## 2005.3534 4.590598236 -35.598471 44.77966778 -56.87328 66.05448
## 2005.3562 6.062425054 -34.126645 46.25149480 -55.40145 67.52630
## 2005.3589 -11.299568257 -51.488638 28.88950169 -72.76345 50.16431
## 2005.3616 -4.931292892 -45.120363 35.25777726 -66.39517 56.53259
## 2005.3644 10.999965659 -29.189105 51.18903601 -50.46391 72.46384
## 2005.3671 8.745706509 -31.443364 48.93477706 -52.71817 70.20959
## 2005.3699 4.763507401 -35.425563 44.95257815 -56.70037 66.22739
## 2005.3726 -4.202190244 -44.391261 35.98688071 -65.66607 57.26169
## 2005.3753 -0.649345017 -40.838416 39.53972614 -62.11323 60.81454
## 2005.3781 3.370809294 -36.818262 43.55988065 -58.09307 64.83469
## 2005.3808 11.633735944 -28.555336 51.82280750 -49.83014 73.09762
## 2005.3836 -7.199646116 -47.388718 32.98942564 -68.66353 54.26424
## 2005.3863 -6.187807773 -46.376880 34.00126419 -67.65169 55.27607
## 2005.3890 -6.551566742 -46.740639 33.63750542 -68.01545 54.91232
## 2005.3918 8.686917821 -31.502155 48.87599018 -52.77696 70.15080
## 2005.3945 3.947583503 -36.241489 44.13665607 -57.51630 65.41147
## 2005.3973 1.214615833 -38.974457 41.40368860 -60.24927 62.67850
## 2005.4000 -1.062335916 -41.251409 39.12673705 -62.52622 60.40155
## 2005.4027 -1.870528889 -42.059602 38.31854428 -63.33441 59.59335
## 2005.4055 -5.313753388 -45.502827 34.87531998 -66.77764 56.15013
## 2005.4082 1.686078435 -38.502995 41.87515200 -59.77781 63.14996
## 2005.4110 6.732946270 -33.456128 46.92202004 -54.73094 68.19683
## 2005.4137 -4.712038561 -44.901113 35.47703541 -66.17592 56.75185
## 2005.4164 -3.321199016 -43.510273 36.86787516 -64.78508 58.14269
## 2005.4192 11.739433482 -28.449641 51.92850786 -49.72445 73.20332
## 2005.4219 2.369557402 -37.819517 42.55863198 -59.09433 63.83344
## 2005.4247 -2.344310137 -42.533385 37.84476464 -63.80820 59.11958
## 2005.4274 -4.828056199 -45.017131 35.36101878 -66.29194 56.63583
## 2005.4301 3.804976526 -36.384099 43.99405171 -57.65891 65.26886
## 2005.4329 15.258119311 -24.930956 55.44719469 -46.20577 76.72201
## 2005.4356 4.041047614 -36.148028 44.23012320 -57.42284 65.50493
## 2005.4384 -20.267566373 -60.456642 19.92150941 -81.73145 41.19632
## 2005.4411 -7.155687836 -47.344764 33.03338815 -68.61958 54.30820
## 2005.4438 1.895808570 -38.293268 42.08488476 -59.56808 63.35970
## 2005.4466 12.439120205 -27.749956 52.62819659 -49.02477 73.90301
## 2005.4493 4.917837084 -35.271240 45.10691367 -56.54605 66.38173
## 2005.4521 4.752437341 -35.436639 44.94151413 -56.71145 66.21633
## 2005.4548 -0.918585749 -41.107663 39.27049124 -62.38247 60.54530
## 2005.4575 0.890125652 -39.298952 41.07920284 -60.57376 62.35402
## 2005.4603 0.788916716 -39.400161 40.97799411 -60.67497 62.25281
## 2005.4630 -2.224609855 -42.413687 37.96446774 -63.68850 59.23928
## 2005.4658 0.195491553 -39.993586 40.38456935 -61.26840 61.65938
## 2005.4685 10.283187554 -29.905890 50.47226555 -51.18070 71.74708
## 2005.4712 -0.590986679 -40.780065 39.59809152 -62.05488 60.87290
## 2005.4740 -4.062571494 -44.251650 36.12650691 -65.52646 57.40132
## 2005.4767 -0.740515476 -40.929594 39.44856313 -62.20441 60.72338
## 2005.4795 10.785741737 -29.403337 50.97482054 -50.67815 72.24963
## 2005.4822 6.895598254 -33.293481 47.08467726 -54.56829 68.35949
## 2005.4849 -7.876892225 -48.065971 32.31218698 -69.34078 53.58700
## 2005.4877 -8.378733784 -48.567813 31.81034562 -69.84263 53.08516
## 2005.4904 -6.135640188 -46.324720 34.05343942 -67.59953 55.32825
## 2005.4932 -3.140599854 -43.329680 37.04847996 -64.60449 58.32329
## 2005.4959 4.872664912 -35.316415 45.06174492 -56.59123 66.33656
## 2005.4986 0.471194505 -39.717886 40.66027472 -60.99270 61.93509
## 2005.5014 1.819876977 -38.369203 42.00895739 -59.64402 63.28377
## 2005.5041 0.260866590 -39.928214 40.44994721 -61.20303 61.72476
## 2005.5068 0.652872013 -39.536209 40.84195283 -60.81102 62.11677
## 2005.5096 3.158157520 -37.030923 43.34723854 -58.30574 64.62205
## 2005.5123 -4.899607996 -45.088689 35.28947322 -66.36350 56.56429
## 2005.5151 -14.255848780 -54.444930 25.93323264 -75.71974 47.20805
## 2005.5178 -5.346161444 -45.535243 34.84292018 -66.81006 56.11773
## 2005.5205 -0.130601655 -40.319683 40.05848017 -61.59450 61.33329
## 2005.5233 -1.429946630 -41.619029 38.75913539 -62.89384 60.03395
## 2005.5260 -3.520436698 -43.709519 36.66864553 -64.98433 57.94346
## 2005.5288 -4.423084011 -44.612166 35.76599842 -65.88698 57.04081
## 2005.5315 6.860193016 -33.328890 47.04927564 -54.60370 68.32409
## 2005.5342 12.305945063 -27.883138 52.49502789 -49.15795 73.76984
## 2005.5370 8.377967953 -31.811115 48.56705098 -53.08593 69.84187
## 2005.5397 -9.578199522 -49.767283 30.61088371 -71.04210 51.88570
## 2005.5425 -11.869938832 -52.059022 28.31914460 -73.33384 49.59396
## 2005.5452 -6.124843841 -46.313927 34.06423979 -67.58874 55.33906
## 2005.5479 5.153006412 -35.036077 45.34209025 -56.31089 66.61691
## 2005.5507 5.680054223 -34.509030 45.86913826 -55.78385 67.14395
## 2005.5534 -8.809371753 -48.998456 31.37971248 -70.27327 52.65453
## 2005.5562 -8.043412560 -48.232497 32.14567188 -69.50731 53.42049
## 2005.5589 6.938560688 -33.250524 47.12764533 -54.52534 68.40246
## 2005.5616 0.317952259 -39.871133 40.50703710 -61.14595 61.78185
## 2005.5644 0.589263475 -39.599822 40.77834852 -60.87464 62.05317
## 2005.5671 0.040700618 -40.148385 40.22978586 -61.42320 61.50460
## 2005.5699 -1.392503849 -41.581589 38.79658160 -62.85641 60.07140
## 2005.5726 -10.096538067 -50.285624 30.09254758 -71.56044 51.36736
## 2005.5753 1.172272123 -39.016814 41.36135797 -60.29163 62.63617
## 2005.5781 3.011391289 -37.177695 43.20047734 -58.45251 64.47529
## 2005.5808 -5.249462129 -45.438548 34.93962412 -66.71337 56.21444
## 2005.5836 -0.009372358 -40.198459 40.17971409 -61.47328 61.45453
## 2005.5863 9.973797669 -30.215289 50.16288432 -51.49011 71.43770
## 2005.5890 11.337201906 -28.851885 51.52628876 -50.12670 72.80111
## 2005.5918 1.363517866 -38.825569 41.55260492 -60.10039 62.82742
## 2005.5945 -6.679088233 -46.868175 33.50999902 -68.14299 54.78482
## 2005.5973 -10.078155251 -50.267243 30.11093221 -71.54206 51.38575
## 2005.6000 -3.494046882 -43.683135 36.69504078 -64.95795 57.96986
## 2005.6027 0.365457595 -39.823630 40.55454546 -61.09845 61.82936
## 2005.6055 1.321938136 -38.867150 41.51102620 -60.14197 62.78584
## 2005.6082 0.259100699 -39.929988 40.44818896 -61.20481 61.72301
## 2005.6110 5.211858549 -34.977230 45.40094701 -56.25205 66.67577
## 2005.6137 0.230382593 -39.958706 40.41947126 -61.23352 61.69429
## 2005.6164 -11.280004609 -51.469093 28.90908426 -72.74391 50.18390
## 2005.6192 -9.558929989 -49.748019 30.63015908 -71.02284 51.90498
## 2005.6219 8.960930222 -31.228159 49.15001949 -52.50298 70.42484
## 2005.6247 -0.781462540 -40.970552 39.40762693 -62.24537 60.68245
## 2005.6274 -10.276035813 -50.465125 29.91305386 -71.73994 51.18787
## 2005.6301 -14.015221099 -54.204311 26.17386877 -75.47913 47.44869
## 2005.6329 7.102783580 -33.086306 47.29187366 -54.36113 68.56669
## 2005.6356 4.806113672 -35.382977 44.99520395 -56.65780 66.27002
## 2005.6384 -16.413671966 -56.602762 23.77541851 -77.87758 45.05024
## 2005.6411 -0.714025543 -40.903116 39.47506514 -62.17794 60.74988
## 2005.6438 16.152691648 -24.036399 56.34178253 -45.31122 77.61660
## 2005.6466 10.212896722 -29.976194 50.40198780 -51.25101 71.67681
## 2005.6493 -6.692916168 -46.882007 33.49617512 -68.15683 54.77099
## 2005.6521 -3.369177506 -43.558269 36.81991398 -64.83309 58.09473
## 2005.6548 1.636830061 -38.552262 41.82592175 -59.82708 63.10074
## 2005.6575 12.876453072 -27.312639 53.06554496 -48.58746 74.34037
## 2005.6603 3.065502726 -37.123589 43.25459481 -58.39841 64.52942
## 2005.6630 -11.041156105 -51.230248 29.14793618 -72.50507 50.42276
## 2005.6658 -6.676852735 -46.865945 33.51223976 -68.14077 54.78706
## 2005.6685 15.775552886 -24.413540 55.96464558 -45.68836 77.23947
## 2005.6712 -6.437295515 -46.626388 33.75179738 -67.90121 55.02662
## 2005.6740 -4.519579817 -44.708673 35.66951328 -65.98349 56.94433
## 2005.6767 -0.550572890 -40.739666 39.63852041 -62.01449 60.91334
## 2005.6795 -13.364800765 -53.553894 26.82429273 -74.82872 48.09911
## 2005.6822 -23.695929400 -63.885023 16.49316430 -85.15984 37.76799
## 2005.6849 14.651046788 -25.538047 54.84014069 -46.81287 76.11496
## 2005.6877 25.348432274 -14.840662 65.53752638 -36.11548 86.81235
## 2005.6904 11.883488878 -28.305605 52.07258318 -49.58043 73.34740
## 2005.6932 -0.444430854 -40.633525 39.74466365 -61.90835 61.01949
## 2005.6959 -3.640901748 -43.829996 36.54819296 -65.10482 57.82301
## 2005.6986 -7.302176963 -47.491272 32.88691794 -68.76609 54.16174
## 2005.7014 -3.641106308 -43.830201 36.54798880 -65.10502 57.82281
## 2005.7041 -2.972993469 -43.162089 37.21610184 -64.43691 58.49092
## 2005.7068 -6.482059185 -46.671155 33.70703633 -67.94598 54.98186
## 2005.7096 3.197266485 -36.991829 43.38636220 -58.26665 64.66118
## 2005.7123 4.045585404 -36.143511 44.23468132 -57.41833 65.50950
## 2005.7151 -15.747323203 -55.936419 24.44177291 -77.21124 45.71660
## 2005.7178 -0.359501137 -40.548597 39.82959518 -61.82342 61.10442
## 2005.7205 14.939584253 -25.249512 55.12868077 -46.52433 76.40350
## 2005.7233 -0.420247627 -40.609344 39.76884909 -61.88417 61.04367
## 2005.7260 -4.405194451 -44.594291 35.78390247 -65.86911 57.05873
## 2005.7288 -7.162702058 -47.351799 33.02639506 -68.62662 54.30122
## 2005.7315 29.473710313 -10.715387 69.66280764 -31.99021 90.93763
## 2005.7342 7.289043929 -32.900054 47.47814145 -54.17488 68.75296
## 2005.7370 14.753126927 -25.435971 54.94222465 -46.71079 76.21705
## 2005.7397 -11.318599800 -51.507698 28.87049813 -72.78252 50.14532
## 2005.7425 -8.433247773 -48.622346 31.75585035 -69.89717 53.03067
## 2005.7452 -5.549215673 -45.738314 34.63988266 -67.01314 55.91471
## 2005.7479 -23.085363008 -63.274462 17.10373552 -84.54929 38.37856
## 2005.7507 2.687074838 -37.502024 42.87617357 -58.77685 64.15100
## 2005.7534 10.355443743 -29.833655 50.54454268 -51.10848 71.81937
## 2005.7562 6.474768021 -33.714331 46.66386715 -54.98916 67.93869
## 2005.7589 9.017072063 -31.172027 49.20617140 -52.44685 70.48100
## 2005.7616 -0.313049178 -40.502149 39.87605036 -61.77697 61.15087
## 2005.7644 -18.192051078 -58.381151 21.99704866 -79.65598 43.27187
## 2005.7671 -4.668004332 -44.857104 35.52109561 -66.13193 56.79592
## 2005.7699 4.242212012 -35.946888 44.43131215 -57.22171 65.70614
## 2005.7726 13.326952157 -26.862148 53.51605250 -48.13697 74.79088
## 2005.7753 11.868349688 -28.320751 52.05745023 -49.59558 73.33227
## 2005.7781 10.038751220 -30.150350 50.22785196 -51.42517 71.50268
## 2005.7808 -6.022435168 -46.211536 34.16666578 -67.48636 55.44149
## 2005.7836 -1.493373840 -41.682475 38.69572731 -62.95730 59.97055
## 2005.7863 -3.863657776 -44.052759 36.32544357 -65.32758 57.60027
## 2005.7890 28.491806026 -11.697296 68.68090758 -32.97212 89.95573
## 2005.7918 23.366433533 -16.822668 63.55553528 -38.09749 84.83036
## 2005.7945 -2.025033965 -42.214136 38.16406799 -63.48896 59.43889
## 2005.7973 -10.115874669 -50.304977 30.07322748 -71.57980 51.34805
## 2005.8000 -22.120572462 -62.309675 18.06852989 -83.58450 39.34336
## 2005.8027 -18.633097093 -58.822200 21.55600546 -80.09703 42.83083
## 2005.8055 11.472170479 -28.716932 51.66127324 -49.99176 72.93610
## 2005.8082 -4.452967296 -44.642070 35.73613566 -65.91690 57.01096
## 2005.8110 -2.088101534 -42.277205 38.10100163 -63.55203 59.37583
## 2005.8137 -30.804157815 -70.993261 9.38494555 -92.26809 30.65977
## 2005.8164 7.067409895 -33.121694 47.25651346 -54.39652 68.53134
## 2005.8192 3.712546384 -36.476557 43.90165015 -57.75138 65.17648
## 2005.8219 7.572529095 -32.616575 47.76163306 -53.89140 69.03646
## 2005.8247 28.150278060 -12.038826 68.33938223 -33.31365 89.61421
## 2005.8274 -15.603545637 -55.792650 24.58555873 -77.06748 45.86039
## 2005.8301 -16.207408604 -56.396513 23.98169596 -77.67134 45.25652
## 2005.8329 -10.645241814 -50.834347 29.54386296 -72.10917 50.81869
## 2005.8356 35.710018195 -4.479087 75.89912317 -25.75391 97.17395
## 2005.8384 3.689909279 -36.499196 43.87901445 -57.77402 65.15384
## 2005.8411 -35.408441562 -75.597547 4.78066381 -96.87237 26.05549
## 2005.8438 11.358040410 -28.831065 51.54714598 -50.10589 72.82197
## 2005.8466 38.429973769 -1.759132 78.61907955 -23.03396 99.89391
## 2005.8493 24.063058391 -16.126048 64.25216437 -37.40088 85.52699
## 2005.8521 -5.787126206 -45.976232 34.40197997 -67.25106 55.67681
## 2005.8548 -22.784474795 -62.973581 17.40463159 -84.24841 38.67946
## 2005.8575 -1.968019962 -42.157127 38.22108662 -63.43195 59.49591
## 2005.8603 -37.829400588 -78.018507 2.35970620 -99.29334 23.63453
## 2005.8630 -40.123969149 -80.313076 0.06513784 -101.58790 21.33997
## 2005.8658 20.501802312 -19.687305 60.69090950 -40.96213 81.96574
## 2005.8685 35.038623064 -5.150484 75.22773045 -26.42531 96.50256
## 2005.8712 13.309700314 -26.879407 53.49880790 -48.15424 74.77364
## 2005.8740 -4.899793566 -45.088901 35.28931422 -66.36373 56.56414
## 2005.8767 -10.019477766 -50.208586 30.16963022 -71.48341 51.44446
## 2005.8795 24.652504530 -15.536604 64.84161272 -36.81143 86.11644
## 2005.8822 4.821624372 -35.367484 45.01073277 -56.64231 66.28556
## 2005.8849 -4.247618128 -44.436727 35.94149047 -65.71156 57.21632
## 2005.8877 -12.995706907 -53.184816 27.19340189 -74.45964 48.46823
## 2005.8904 -2.966753841 -43.155863 37.22235516 -64.43069 58.49718
## 2005.8932 16.489091830 -23.700017 56.67820103 -44.97485 77.95303
## 2005.8959 -8.341499713 -48.530609 31.84760969 -69.80544 53.12244
## 2005.8986 6.585693797 -33.603416 46.77480340 -54.87825 68.04963
## 2005.9014 -21.514480942 -61.703591 18.67462886 -82.97842 39.94946
## 2005.9041 6.866791027 -33.322319 47.05590103 -54.59715 68.33073
## 2005.9068 -8.491147167 -48.680257 31.69796304 -69.95509 52.97279
## 2005.9096 7.366899570 -32.822211 47.55600998 -54.09704 68.83084
## 2005.9123 -14.278205782 -54.467316 25.91090483 -75.74215 47.18573
## 2005.9151 -29.059196359 -69.248307 11.12991445 -90.52314 32.40474
## 2005.9178 20.403320040 -19.785791 60.59243105 -41.06062 81.86726
## 2005.9205 6.991772363 -33.197339 47.18088357 -54.47217 68.45571
## 2005.9233 18.493458337 -21.695653 58.68256975 -42.97048 79.95740
## 2005.9260 18.176142134 -22.012969 58.36525375 -43.28780 79.64008
## 2005.9288 12.451507815 -27.737604 52.64061963 -49.01243 73.91545
## 2005.9315 1.251708469 -38.937404 41.44082049 -60.21223 62.71565
## 2005.9342 33.475024666 -6.714088 73.66413688 -27.98892 94.93897
## 2005.9370 -18.313315940 -58.502428 21.87579648 -79.77726 43.15063
## 2005.9397 -4.757711441 -44.946824 35.43140118 -66.22166 56.70623
## 2005.9425 -2.387925109 -42.577038 37.80118771 -63.85187 59.07602
## 2005.9452 15.986501530 -24.202611 56.17561455 -45.47744 77.45045
## 2005.9479 1.441643683 -38.747470 41.63075691 -60.02230 62.90559
## 2005.9507 -4.207474292 -44.396588 35.98163913 -65.67142 57.25647
## 2005.9534 5.818011203 -34.371102 46.00712483 -55.64593 67.28196
## 2005.9562 -5.612617543 -45.801731 34.57649629 -67.07656 55.85133
## 2005.9589 7.995900077 -32.193214 48.18501411 -53.46805 69.45985
## 2005.9616 0.870249733 -39.318864 41.05936396 -60.59370 62.33420
## 2005.9644 -1.485733515 -41.674848 38.70338092 -62.94968 59.97821
## 2005.9671 4.522164280 -35.666950 44.71127891 -56.94178 65.98611
## 2005.9699 20.927021402 -19.262093 61.11613624 -40.53693 82.39097
## 2005.9726 10.719934566 -29.469180 50.90904960 -50.74401 72.18388
## 2005.9753 -17.023367657 -57.212483 23.16574758 -78.48732 44.44058
## 2005.9781 -28.848344045 -69.037459 11.34077139 -90.31229 32.61560
## 2005.9808 -32.141652930 -72.330769 8.04746271 -93.60560 29.32230
## 2005.9836 -15.207289173 -55.396405 24.98182667 -76.67124 46.25666
## 2005.9863 2.797376773 -37.391739 42.98649282 -58.66657 64.26133
## 2005.9890 4.351510375 -35.837606 44.54062662 -57.11244 65.81546
## 2005.9918 14.270432014 -25.918684 54.45954846 -47.19352 75.73438
## 2005.9945 -2.076693282 -42.265810 38.11242336 -63.54064 59.38726
## 2005.9973 12.836645857 -27.352471 53.02576270 -48.62730 74.30060
## 2006.0000 -16.715050963 -56.904168 23.47406609 -78.17900 44.74890
## 2006.0027 3.020884290 -37.168233 43.21000154 -58.44307 64.48484
## 2006.0055 7.999234299 -32.189883 48.18835175 -53.46472 69.46319##NOTE: AIC = 31986.86 , BIC = 32003.94, RMSE = 31.34532
Also, the headline of the plot below contains ETS(A,N,N) showing that the automated model characterized error of the “tsWSR_PK” SERIES as Additative (A), trend as None (A) and seasonality as None (N) which is equivalent to simple exponential model(ses) with only alpha parameter i.e level.
#Model 2 : ARIMA Model(AutoRegressive Moving Average) It is used for forecasting for both seasonal and non- seasonal level.
#2.1 Auto Arima model without sesonality:
set.seed(301)
model_Var11 <- auto.arima(train10, seasonal = FALSE)
summary(model_Var11)## Series: train10
## ARIMA(2,0,2) with zero mean
##
## Coefficients:
## ar1 ar2 ma1 ma2
## 0.6267 -0.1022 -0.4235 -0.3696
## s.e. 0.0495 0.0509 0.0468 0.0491
##
## sigma^2 estimated as 1016: log likelihood=-10702.27
## AIC=21414.55 AICc=21414.57 BIC=21443.01
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -0.4976616 31.85287 22.96835 NaN Inf 0.6275488 0.0004603258##NOTE: AIC = 21414.55, BIC = 21443.01, RMSE = 31.85287
tsdisplay(residuals(model_Var11), lag.max = 45, main = '(1,1,1) Model Residuals')
#2.2 Auto Arima model with sesonality:
set.seed(301)
model2_Var11 <- auto.arima(train10, seasonal= TRUE)
summary(model2_Var11)## Series: train10
## ARIMA(4,0,2) with zero mean
##
## Coefficients:
## ar1 ar2 ar3 ar4 ma1 ma2
## 0.3504 0.2212 -0.1638 0.0722 -0.1467 -0.6358
## s.e. 0.1240 0.1421 0.0764 0.0433 0.1213 0.1155
##
## sigma^2 estimated as 1016: log likelihood=-10701.17
## AIC=21416.34 AICc=21416.39 BIC=21456.19
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -0.5104428 31.83673 22.95572 NaN Inf 0.6272036 0.0003918353##NOTE: AIC = 21416.34, BIC = 21456.19, RMSE = 31.83673
tsdisplay(residuals(model2_Var11), lag.max = 20, main = 'Seasonal Model Residuals')
#Plotting forecast for each model
par(mfrow = c(2,2))
fit_auto_train_Var11 %>% forecast(h=341) %>% autoplot() 
model2_Var11 %>% forecast(h=341) %>% autoplot() 
model_Var11 %>% forecast(h=341) %>% autoplot() 
COMMENT:
1. The plots includes 80% to 95% confidence interval.
2. For ARIMA models it plots the forecast but because of the nature of autoregressive process of 1 lag i.e. AR1, these forecast stabilizes quite smoothly.
Plot and comment on the residuals of the fitted data for both models in the same plot.
Residual Plot - to confirm no problem with this model
par(mfrow= c(3,2))
hist(fit_auto_train_Var11$residuals,col = 'red',xlab = 'Error',main = 'Histogram Of Residuals',freq= FALSE)
lines(density(fit_auto_train_Var11$residuals))
hist(model_Var11$residuals,col = 'red',xlab = 'Error',main = 'Histogram Of Residuals',freq= FALSE)
lines(density(model_Var11$residuals))
hist(model2_Var11$residuals,col = 'red',xlab = 'Error',main = 'Histogram Of Residuals',freq= FALSE)
lines(density(model2_Var11$residuals))
OBSERVATION: The residuals for each model are normally distributed, which shows the good fit of the models. It is normally distrbuted
Testing the autocorrelation and partial autocorrelation of the residuals (using the plots and Ljung-Box Q statistic) up to an appropriate lag *
#ACF & PACF PLOTS
par(mfrow = c(3,2))
acf(fit_auto_train_Var11$residuals, main = 'Correlogram')
pacf(fit_auto_train_Var11$residuals, main = 'Partial Corelogram')
acf(model_Var11$residuals, main = 'Correlogram')
pacf(model_Var11$residuals, main = 'Partial Corelogram')
acf(model2_Var11$residuals, main = 'Correlogram')
pacf(model2_Var11$residuals, main = 'Partial Corelogram')
NOTE:
1. Residuals are the difference between actaual and fitted values
2. These blue lines are signficance bounds
3. This graph shows us the autocorelations for insample forecast errors
4. Do not exceed these significance bounds for lags 1 to end
- Ljunx-Box Test to check the autocorelations of the residuals
This test used to test the lack of fit of a time series model.
This test is applied to the residuals of the time series model,
HO: No serial correlation upto 20 lags (does not exhibit lack of fit of the model)
Ha: Serial corelation is present (the model exhibits lack of fit)
We reject the null hypothesis, if p value is less than 0.05. This test is generally done for ARIMA models
Box.test(model_Var11$residuals, lag =20, type = 'Ljung-Box')##
## Box-Ljung test
##
## data: model_Var11$residuals
## X-squared = 16.732, df = 20, p-value = 0.6703Box.test(model2_Var11$residuals, lag =20, type = 'Ljung-Box')##
## Box-Ljung test
##
## data: model2_Var11$residuals
## X-squared = 14.525, df = 20, p-value = 0.8029OBSERVATIONS:
For above performed Ljunx-Box Test on ARIMA models output, we can say that p-value is more than significance level 0.05, then there is not a statistical significance.
We conclude that there is a little evidence of non-zero auto-corelations in the insample forecast errors at lags 1 to 20.
So we fail to rejects the null hypothesis. Hence, we conclude that there is no serial auto corelation present between lags. Hence, the model seems to be good fit.
Test and comment on the normality of the residuals.
Here, further testing the normality by plotting Normal Q-Q plots. From below plots we observed that most of the datapoints lies on the line. Hence, we could conclude that our model produces residuals that are normal
par(mfrow = c(2,2))
qqnorm(fit_auto_train_Var11$residuals)
qqnorm(model_Var11$residuals)
qqnorm(model2_Var11$residuals)
Validating The Model by testing the model performance with Holdout set
Here, choosing RMSE as evaluation parameter. The lower RMSE indicates a more accurate forecast.
Below, is the comparison of model. We are fitting the model to test set which is the holdout set. And checking the accuracy using RMSE(Root mean square error) as an evaluation parameter.
accuracy(forecast(fit_auto_train_Var11), test10) ["Test set", "RMSE"]## [1] 39.2348#o/p - 39.2348accuracy(forecast(model_Var11), test10) ["Test set", "RMSE"]## [1] 34.85059#O/P - 34.85059accuracy(forecast(model2_Var11), test10) ["Test set", "RMSE"]## [1] 34.81429#o/p - 34.81429accuracy(forecast(model_Var11), test10) ["Test set", "RMSE"]## [1] 34.85059#O/P - 34.81429NOTE:- Here, the RMSE value is less for ARIMA models compared to exponential model.
The minimum RMSE is of “model2_Var11”
COMMENT ON BEST MODEL AND ITS PARAMETERS
We observed the best model to be ARIMA model i.e.“model2_Var11”.
summary(model2_Var11)## Series: train10
## ARIMA(4,0,2) with zero mean
##
## Coefficients:
## ar1 ar2 ar3 ar4 ma1 ma2
## 0.3504 0.2212 -0.1638 0.0722 -0.1467 -0.6358
## s.e. 0.1240 0.1421 0.0764 0.0433 0.1213 0.1155
##
## sigma^2 estimated as 1016: log likelihood=-10701.17
## AIC=21416.34 AICc=21416.39 BIC=21456.19
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -0.5104428 31.83673 22.95572 NaN Inf 0.6272036 0.0003918353For the best model ARIMA(4,0,2) ,which means
p = 4
d = 0
q = 2
For the best model, 4 members of lag are used as a predictor. As the series is stationary so members of differences needed for stationarity is 0.
2 are the number of lagged forecasts errors used in the prediction equation.
AIC = 21416.34, RMSE = 31.83673 which is minimum as compared to other models. AICc(corrected AIC) = 21416.39
REFERENCES
[1] https://cran.r-project.org/web/packages/imputeTS/vignettes/imputeTS-Time-Series-Missing-Value-Imputation-in-R.pdf
[2] https://www.kaggle.com/juejuewang/handle-missing-values-in-time-series-for-beginners
[3] https://towardsdatascience.com/how-to-handle-missing-data-8646b18db0d4
[4] https://otexts.com/fpp2/missing-outliers.html
[5] https://www.analyticsvidhya.com/blog/2018/09/non-stationary-time-series-python/
[6] https://johannesmehlem.com/blog/exponential-smoothing-time-series-forecasting-r/
[7] Lecture Notes